Pupils'+contribution

Dear pupils,

If you have any math puzzles or quizzes to recommend to your friends, please post them below with your name written. You are responsible to look at your respondents' answers to your questions and give your comments. Each different puzzle or question should be separated by a line.

Please keep your discussion to the math question concerned and do not add irrelevant comments. You can create a discussion page for further elaboration on any question.

Mdm Teo

Form the numbers 40 to 75 using 2 or more of the numbers 1,2,3,4 and 5. Each number can only be used once. Only the basic four operations and brackets are allowed. (It is possible.)

Kheng Hun

If I use 2 numbers, e.g. 2 and 3 to form 23, is it allowed? ZX

Sorry, forgot to state the restrictions.

Kheng Hun

Can I answer like this: 40 = 2 x 4 x 5 Isaac

State the restrictions! ZX

Ya, if not it would be very easy! ~Isaac

What number equates to the sum of the factorials of its digits? ZX

Hello? My question is the same as this one. It is right at the bottom of the page. Rayner

Sorry. Don't answer this qn. ZX

What number has 25 digits and divides by 25 and if you just take the first //n// digits, the result will divide by //n//? ZX P.S. Don't answer or tell anyone the answer for all of my question, Rayner.

Why? The answer is 3608528850368400786036725 Rayner

Cos u know all the ans. ZX

Does that mean that anybody who knows the answer cannot answer? Rayner

Come on! I'll explain to you in school on Mon? ZX

The number is ** 3,608,528,850,368,400,786,036,725. ~ ** Isaac

Heh Heh Heh. Isaac, you copied it from ***... and you forgotten to change the font colour! Rayner P.S.** * is just a website that is a secret. And I really wondered if anybody actually spotted that I had written the answer a long time ago.

Oh sorry. I didn't bother changing the colour. Anyway a clue to where I got his from: puf ~Isaac

Rayner gets the credit. (his answer's in white) ZX

Can you make **all** the numbers from 101-200 using 4 4's and any operators except squares, cubes... but 'to the power of' is allowed. ZX

The answer is no. Most numbers are not possible.

My list so far:

104= 4*4!+4+4 108= (4!+4)*4-4 116= (4!+4)*4+4 128= 4*4*(4+4)

Is 44 allowed?

Kheng Hun

102= 4*4!+4!/4 104= 4*4!+4+4 108= 4*4!+4!/SQRT4 111= 444/4 112= 4*4!+4*4 116= (4+4/4)!-4 118= (4+4/4)!-SQRT4 120= ((4*4+4)/4)! 121= (44/4)^SQRT4 122= (4+4/4)!+SQRT4 124= (4+4/4)!+4 126= (4^4/SQRT4)-SQRT4 128= 4*4*4*SQRT4 130= (4^4/SQRT4)+SQRT4 132= (4^4/SQRT4)+4 138= (((4!)^SQRT4)-4!)/4 140= ((4!)^SQRT4)/4-4 142= ((4!)^SQRT4)/4-SQRT4 143= (((4!)^SQRT4)-4)/4 144= (SQRT4+SQRT4+SQRT4)*4! 145= (((4!)^SQRT4)+4)/4 146= ((4!)^SQRT4)/4+SQRT4 148= ((4!)^SQRT4)/4+4 150= (((4!)^SQRT4)+4!)/4 156= (4!+SQRT4)*(4!/4) 160= (44-4)*4 169= ((4!+SQRT4)/SQRT4)^SQRT4 172= (44*4)-4 174= (44*4)-SQRT4 176= 44*SQRT4*SQRT4 178= (44*4)+SQRT4 180= (44*4)+4 Rayner (please help me check for mistakes)

(To Kheng Hun: Yes. ZX)

A wine importer received a large consignment of bottles of wine from his favourite vineyard.

What is the smallest number of bottles the wine importer had when he started? Zheng Xian P.S. Can somebody answer these 2 questions?
 * He immediately celebrated by drinking one of the bottles.
 * The day after receiving the wine he sold exactly a fifth of the remaining bottles, which was a good enough excuse to treat himself to a second bottle.
 * On the third day he again sold exactly one fifth of the bottles he had in stock at the beginning of the day. So again he celebrated with a bottle for himself.
 * This pattern continued until the end of the seventh day, when the number of bottles left no longer made it possible for him to dispose of a fifth of them on the eighth day.

15621? Rayner

Correct! ZX

How many different ways can you cover a chessboard with 32 dominoes? Zheng Xian P.S. Is it too hard?

I think it came out in a Murderous Maths book. Rayner

It did??? Zheng Xian

Yes. It came out in More Murderous Maths, but now the title has been changed to Guaranteed to Mash your Mind. Rayner

I found it but it was not the same qn. yes, i noe, it was bout dominoes + chessboard, but it wasn't the same. ZX P.S. i dun think dis came out in an MM book.

12988816? Rayner

What's with the question marks when you know you are bound to be correct?! ZX

Rayner is correct. This was printed out in Muderous Maths: Numbers, the Key to the Universe. Jeremy

Told you so. Rayner

Fine. ZX


 * This question came out in the 2009 PSLE Math Paper. The paper was described as 'unbelievably tough'.**

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?

Isaac

Sweet to Chocolate || Ken Sweet to Chocolate || This table gives 2 statements: x+12 = y 4y+18 = 7x Using substitution, you get a third statement: 4x+48+18 = 7x You simplify it to get a fourth statement: 3x = 66 x = 22 Since x = 22, y is 22+12, which is 34. 2y is 34*2, which is 68, which is the number of sweets Ken bought.
 * Jim
 * x : 7x || y : 4y ||
 * x+12 : 7x || y : 4y+18 ||
 * x+12 : 14x || y : 4y+18-7x ||
 * x+12-y : 14x || 2y : 4y+18-7x ||

And if you want to know how many chocolates Jim bought, you take 22*14, which is 308. (In my opinion, Jim is very greedy.) In the end, Jim had 22 sweets and 154 chocolates, Ken had 34 sweets and 136 chocolates and the conditions are met. Rayner

Good! Then do you rate this question as 'unbelievably tough'? ~Isaac

It is a little difficult but not to the extreme like unbelievably tough. Rayner

Actually, instead of using all those 'x's, you could simply use normal terms. here's what I did. But it's actually quite the same. Anyway, this is just how I solved the question. 7(S-12) = C 4S = C-18 C = 4S + 18 7S-84 = 4S +18 7S = 4S +18+84 3S = 102 S = 34 34 X 2 = 68 ~Alex
 * S means sweets, and C means chocolates.**
 * Hence, the answer is 68.**

How many fibonacci numbers are there from 1 to 30000? Zhia Yang

And btw, I just created this program. If you are REALLY stuck, use this.

EDIT: I just made this program. Just 4 fun.

Ok so this is the fibonacci thing.

Wow nice! How did you make it? QBasic? Visual Basic? Isaac

Command line scripting(batch) + C++ Zhia Yang

Your prime number generator thing cannot work. It gives a whole lot of gibberish. Rayner

Uh-Huh It starts at 11, goes all the way until 37625, and dissapears right? It's a glitch or bug in the program.

Hi Zhia Yang. Great Generators. But the bad thing was, I accidentally typed 'a' in your fibonacci generator, and *ahem* ~Jarret

Uh-Huh, *ahem* Zhia Yang

Yes. If you type letters, *BAM!* and the thing **__NEVER__** stops! Rayner

So, don't! Zhia Yang

And the limit is 46 Fibonacci numbers if you input only numbers. By the way, the 46th Fibonacci number is 1836311903. Rayner

In the principality of a country, the currency is the Dollar which is worth 100 Cents. The Bank has just issued the new One Dollar note, but now want a coin system for the Cents. The plan is that you should be able to make ANY amount between 1 and 100 Cents by using just one or two coins. (The two coins can be the same or different.) What is the smallest number of different coins they need for their new system - and what are they? Zheng Xian

18 coins. 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90

Kheng Hun

Wrong! ZX

If you can have more than two coins but the coins can only be used once, I know the answer. __7__ Rayner

What do you mean? You can only use up to 2 coins and they can be the same. ZX

If you can only use up to 2 coins, I don't see how Kheng Hun's answer is wrong. Is there a way to reduce the number even further? Isaac

Yes. ZX

I got another answer. But it is still the same number of coins. 1 2 3 4 5 6 7 8 9 11 21 31 41 51 61 71 81 91 Isaac

16 coins! 1,3,4,9,11,16,20,25,30,34,39,41,46,47,49,50 Rayner

Correct! ZX

I got another one the one before was a fairly easy one get ready 91 63 91! 93 63 82/ 21 73 32 /41 63 63 31! WY

Hint: it has something to do with what a lot of people bring to school but is not allowed at school.

Let me guess. A handphone? Rayner

yes but just solve the code WY

Each pair of numbers decribes a unique letter: the first (2-9) decribes //what number you press,// and the second (1-4) describes //how many times you press it.//

The / is a space, but the ! is what it is: an exclamation mark.

Therefore, the message is: **WOW! YOU ARE GOOD!** Jeremy (PS: I LOVE SUPERSKARMORY)

Oh yah. I totally forgotten about the handphone code. Rayner

/ @# / % / ( / / @% / ! / !$ / & /=separator between letters / /=seperator between words

the code spells my name so don't check the history

The answer is... WEI YANG! Jeremy

Correct but how did you figure this out??? don't tell me u checked the history!!! / @# / % / ( / / @% / ! / !$ / &

jeremy's correct answer is not counted as he figured it out by guessing so someone please tell me how you solve the code.

Shift+1 is ! Shift+2 is @ Shift+3 is # Shift+4 is $ Shift+5 is % Shift+6 is ^ Shift+7 is & Shift+8 is * Shift+9 is ( Shift+0 is ) Then after the conversion you will get this (I removed the / and changed it to -): //23-5-9 25-1-14-7// Then, you follow the substitution code (Basic): A-1, B-2, C-3,..., Y-25, Z-26 And get WEI YANG, which is written by Wei Yang Rayner (:P)

ok... but can u solve the top 1???

What is the sequence 4,3,3,5,4,4,3,5,5,4,3,6,6,8,8,7,7,9,7,8,6,...? Please answer in a week. Jeremy

Today in school, Isaac asked me a few questions concerning logic. I answered them correctly. But I thought they were fun. For those who haven't heard of it from Isaac, you may answer them.

1) You are racing. You overtake the person in 2nd place. What position are you in? 2) You are racing. You overtake the person in last place. What position are you in? 3) Mary's father had five sons. Their names are Nana. Nini, Nono, Nene. What is the name of the last son? 4) Mary's father had five daughters. Daadaa, Deedee. DooDoo, DiiDii. What's the name of the last daughter?

Alex

1) You are still in 2nd place!!! 2) You CAN'T overtake someone in last place, unless you are in the -1 place, which is impossible 3) Is Mary mistyped? Its a girl, right? 4) MARY So obvious Zhia Yang

I'M BACK! Answers: (1) Still in 2nd place. (2) It is impossible to say this because there is nothing behind last. //(3) Nunu. (4) Duuduu. Jeremy

1) 1st 2) woohoo (3) Nunu (Mary's a homo) (4) Duuduu (Mary's a homo) ZX (lame answers)

1) 2nd 2) You can't overtake someone in last place 3) Mary 4) Mary ZX (non lame answers)

1)Either 1st or 2nd (You did not state that there is only 1 lap) 2)Any position except last (You still did not state that there is only 1 lap) 3)Have you gone crazy? 4)Mary Rayner//

Oh yeah! Smart thinking Rayner, the 1st person may lap the last person (but the position is not changed) ~Isaac

Hee hee these were sent by Shannon Lee from Mainstream on one of her chain e-mails. There is one more question, but it has already been asked here. (i.e. the 5000+10+20+30+40 one) Isaac

Anyway, Shannon also gave a bonus 5th question, although it is not related to Math, I'll just put it here for you to guess...

A mute person goes into a shop and wants to buy a toothbrush. By imitating the action of brushing his teeth he successfully expresses himself to the shopkeeper and the purchase is done. Next, a blind man comes into the shop who wants to buy a pair of sunglasses; how does he indicate what he wants?

Isaac

He says," I want a pair of sunglasses." Zheng Xian

KE-rrect! Jeremy

There are six people at a party. Prove that 3 of them who know each other or 3 other people who are completely strangers to each other. Adric

How? Isaac

You have eight weights and a weighing scale. All the weights are of the same weight except for one, that is lighter. Using only two weighs on the weighing scale, how do you find out which weight is the lighter one? No guessing is accepted. Alex (This question is taken from a puzzle game, below are images to explain further if you don't understand)



First weigh 1, 2, 3 against 4, 5, 6. If they balance, weigh 7 against 8. The weight on the scale that goes up is lighter. Else: (1, 2, 3 goes up) Weigh 1 against 2. If they balance, 3 is lighter. If one of the sides goes up, the weight on that side is lighter. (4, 5, 6 goes up) Weigh 4 against 5. If they balance, 6 is lighter. If one of the sides goes up, the weight on that side is lighter. Jeremy

Hi Jeremy, yes, you're correct. Congrats :) Alex

Is this one of your Professor something games you showed me when you came to my house in June? Anyway how did you take an image?? Isaac

It is. The name of the game is "Profeesor Layton and the Curious Village". Rayner About 27,700 results (0.15 seconds) Pls view the above diagram. What is 'Y'?? Jarret

Y=9 ZX

Sorry ZX, but you are wrong. (This question was in my sister's P2 Math Assessment!) Jarret

Jarret, I think I know. The sum of each row of the numbers given are: 21, 41, 81. So the first line is 11, if my rule is correct. 11+10=21. 21+20=41. 41+40=81. Alex

Erm - is there any other answer?? (I want to find out all possible answers) Jarret

Cressida didn’t like to tell her age, so when she was asked, her mother answered for her. Her mother said, “I’m just seven times as old as she is now. In twenty years, she will be just half the age that I will be then.” How old is clever little Cressida?

Kai Ren

She's four. Zheng Xian

How is Cressida clever? Her mother answered for her. Rayner

Tim and I can’t seem to get our watches working properly. His consistently runs one minute per hour fast, and mine runs two minutes per hour slow. This morning we nearly missed a wedding because our watches were an hour apart and we looked at the slower one. How many hours had elapsed since we set both of them properly?

Kai Ren

20 hours. Zheng Xian

Decimals palindromes (reverse, add reverse, add)

Anyone knows the palindrome for 9.999, 888.88 and 99.999? Kheng Hun

For 9.999 and 99.999, they can't be made into decimals palindromes. I gave up after getting "MATHS ERROR" on the calculator! Ng Jian Rong

a)What is pie times 2? b)What is the definition of pie? c)Is pie edible? d)If the radius of a circle is 6, what is the circumference? e)How does pie taste like? P.S Ok. Parts c and e are not related to maths... Zhia Yang

Zhia Yang, it's pi not pie. a) 6.283185307... b) Er... What is it? c) A pie is, but pi no. d) 37.69911184 e) Sorry, no answer. Isaac

Ya. Er. Its correct. Zhia Yang

Isaac, actually it depends on the type of pie you ate! Ng Jian Rong

My Answer: a) 2 pies b) Food?? c) Yes, and it is tasty. d) 37.69911184 e) Chicken pie tastes like chicken, apple pie tastes like apple, banana pie tastes like banana, blueberry pie taste like blueberry etc. etc. WY

a)If A=1+1,and B=1+2, and so on, what is "encyclopedia"? P.S add 1 and 1, and put 2 if u want to put A. P.S.S if u get it wrong, its weird. P.S.S.S seperate letters with a "_" aka underscore. P.S.S.S.S Its VERY simple. Zhia Yang

Hey! This was sent by someone on hotmail? It's not related to Maths... Isaac

Ok. Fine. Now answer the second question. Zhia Yang

124? Isaac

NO! its: 6_15_4_26_4_13_16_17_6_5_10_2 Get it? Zhia Yang

There are 1000 lockers in a high school with 1000 students. The problem begins with the first student opening all 1000 lockers; next the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers closed, closes lockers open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and so on. This goes on until every student has had a turn. Which are the lockers that are still open after all 1000 students have gone through?

Kai Ren (This is fiendishly difficult!!!!)

What I know for sure is that the lockers with square numbers will still be open (e.g. 1,4,9,16,25...). Isaac

This answer is correct, but how did u get it??? Pls give me the explanation. Kai Ren

Because a square number has an ODD number of factors. :-) Isaac

What is 10+21+14+Space+4+1=? Relationship with letters. Thats the clue. Well, its super easy! -CANNOT TELL MY NAME- Jun Da Cause i'm not from resillient.

The answer is JUN DA...... its quite obvious, A = 1, B = 2, C = 3, etc YY

Oh yeah! What a trick. Isaac

And do you know who i am???

Jun Da Guess me!

[1-0] X(Times) 1=? Abdul Lateef Isaac,

Yes, but that was not what I was thinking of. I am talking about it physically. Lateef

1 Isaac What do you mean,'physically'? Jeremy

Yeah I don't get 'physically'. Yun Yee

So what's the answer? Isaac

What is half of 8? Timothy

Answer by Rayner: 0,3 and 4 Reason: Cut the '8' vertically in half, you get two 0's. Cut the '8' horizontally in half, you get two 3's. Divide 8 by 2 and you get 4. Yes. Answer by Saaaaarthhhhhhak:0,3,4 The answer is 4, not 0 or 3 OK? Jeremy

Jeremy, It CAN be 0 and 3 too. Physically. Yun Yee OK!But...I was thinking of this...what? Yes, it is that I was thinking about it NBUIFNBUJDBMMZ(this is in code.) Jeremy Jeremy, is that code: 'Mathematically'?? Guess what! I have learnt many of these types of codes. Hooray for me! (JARRET)

It is Mathematically. You just transfer each letter into the letter before it. Yun Yee

Easy code... That's one of the basic codes I learnt. Isaac

yrt ot eolvs shit(not the word 'shit' don't get me wrong) eodc tarrej. Wei Yang

Wei Yang, Your code is : Try to solve this code Jarret. JArret ( YOu should not put your question with someone else's question)

Whatever. Wei Yang

I got another one the one before was a fairly easy one get ready 91 63 91! 93 63 82/ 21 73 32 /41 63 63 31! This is open, anyone can solve it.

DO+YOU+FEEL=LUCKY Write the number sentence in numbers.(Each letter stand for one number) Zheng Xian The answer is:57+870+9441=10368 Jeremy

Correct!!! Zheng Xian

Ha! This is in the Cryptarithms worksheet! Isaac

The following seven numbers have a common property. What is it? 1961 6889 6119 8008 8118 6699 6009 Yun Yee

They have at least one pair of repeated digits. Isaac

Comments from YY: No! Bad luck, guess again. :P

When they are turn upside down they are still the same. Zheng Xian Am I right???

I think so (Isaac).

Yes you are right. o.0

Another answer is that when you split each 4-digit number into 2 2-digit numbers each, when you flip it over horizontally over, you get a symmetrical number. Am I correct? If I am Yay me! I think Zheng Xian is correct. It does make sense!

Yes u are correct. That was another way i worked it out. Yun Yee

A question about probability: suppose you have a typewriter with only the I key on it. Then every time you type a letter, another letter is hammered in. What is the probability that you will type: "To be or not to be, that is the question" randomly typing? Jeremy

Oh Jeremy, that is going to take a reallllllllllllyyyyyyyyy long time!!!!!!!!!!!!!!!! (Plus, I don't feel lucky.) Tricia

No, Tricia, this question came from the Murderous Maths book Do You Feel Lucky (or at least I think it does) Isaac

If you ask me, I think its impossible. If you can only type "I", and only one letter is hammered in, then there must be an 'I' every 2 letters. Right? Well of course unless you type 'I' as the first letter and another letter is hammered in and then the letter that was just hammered in was also counted as an "I" and ANOTHER letter was put in, then its possible. And its impossibe to type randomly. You can only type: iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii. Which is like, SO un random... So Jeremy??? Zhia Yang.

What is 2 + 0 ? Hari

20 (just guessing) Isaac

From Hari : SORRY but you are Wrong :)

Is it 2? Zheng Xian

I think the answer SHUD be 2 coz.... It doesn't even seem like a trick question 2 me. Yun Yee

I thought it was one, so I put 20. Isaac

What do u mean? (YY)

Yeah what do you mean? Zheng Xian

I thought it was a trick question so I thought of an answer and came up with 20 (2 and 0 combined) Answer by Sarthak:Is it 2?????

HARI!!! Is it 2 or not? (YY)

Of course it's 2!!!!!! That's common sense!!!!!Everybody knows there's no such thing as 'trick question' in Math!!!

But, 2+0=10! (can you see why?) Jeremy

Yes I can see why.... Yun Yee

How? I'm puzzled. Isaac

That's because if you do some binary to decimal conversion, the number is 2. Wei Yang

If this is not a trick question, the answer definitely will be 2. Chan Jun Da

Now Hari, will you place the answer or not? Jun Da

The answer is not 2...it is 1010 (do some binary to decimal conversion) Jeremy

how can the answer be 10, are you kidding? Wei Yang

2 in binary is 10, 0 in binary is 0 10+0=10 Rayner

Explanation for my entry F(4) //entries above: It's actually binary **and** binary again! (By the way, Wei Yang is correct!) (...) Jeremy /\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/

Actually, I know the answer to this. If you put the number 2 (with your fingers), it will look like a 'V' And when you put the a '0' on top of the 'V', it will look like a ice-cream. Therefore the answer is ICE CREAM Jarret (FYI Zhia Yang put jarret's name, coz he did not put it. and i checked history:) )

Or rabbit-head, Jarret coz... Like your method, I put the "0" below the "V" and the "V" looks like the ears and the "0" the face Ng Jian Rong.

I was the 1st 2 ans ice cream. ZX//

What is the smallest number can be divided by the numbers 1-100? Zheng Xian

0 Sheldon

Can you give me another number that is not 0? (no negative please) Zheng Xian

Heh, but any number divided by 0 is not a negative number but a indefinite number which equals infinity. Jun Da

1 Isaac

No (Can 1 be divided by 99?) : ) Zheng Xian

If you don't get the exact value, like say two decimal places. It's like pi. Yun Yee

And what do you mean? Zheng Xian

That means u dun need to get the exact amount.

Then the number is very incredibly big. Isaac The answer is 1! :) Jeremy

No, didn't you see what I said to Issac? I said "No (Can 1 be divided by 99?)" : ) Zheng Xian

Answer: 69,720,375,229,712,477,164,533,808,935,312,303,556,800 Jeremy

Err, YES YOU ARE ABSOLUTELY CORRECT!!!!!!!!!!!!!!!!!!!!!!! Zheng Xian

How did Zheng Xian work this out???

Well, he found out the LCM of 1, 2, 3, 4, 5, ..., 98, 99 and 100. (who wrote the post above mine?) Isaac

The LCM is 64*81*25*49*11*13*17*19*23*29*31*37*41*43*47*53*59*61*67*71*73*79*83*89*97 which I do not bother working out Rayner

After a long time of calculation, I computed that the answer is 69 720 375 229 712 477 164 533 808 935 312 303 556 800, which is the same as what Jeremy and Zheng Xian got. *COUGH* *WHEEZE* Rayner

DEVIOUS X 8 = FIENDISH Zheng Xian Answer:6713298 X 8 = 53706384 Jeremy

Correct!!!!! Zheng Xian

Whoa. Jeremy is GOOD. Yun Yee

That means that this puzzle is not devious nor fiendish to Jeremy! Isaac PS: I solved it using an alphametic solver. I entered it as: DEVIOUS+DEVIOUS+DEVIOUS+DEVIOUS+DEVIOUS+DEVIOUS+DEVIOUS+DEVIOUS= FIENDISH Jeremy

How did you find the alphametic solver? On the Internet? Isaac It __was__ on the Internet.Who was talking about the Big Bang and the Big Crunch? Jeremy

What Big Bang, what big Crunch? Isaac

Sorry. Jeremy

946 + 483 + 9684 = 10168 Add just __one__ line without doing anything else to make this statement true. Rayner

946 + 483 + 9684 ≠10168 Alex

RC:You are not supposed to put the 'does not equal' sign

I forgot to tell you that.This is hard! I can only say that Alex is correct. Isaac

There is no solution to this puzzle! Jeremy

Is there a misprint? If 483 is 484, all you need to do is to cancel the "946"! Sheldon Probably... Jeremy

How come there is nobody solving my puzzle??? I used the calculator and checked a googolplaxian times and it always showed the same answer. It cannot be wrong P.S. The numbers were not chosen by me. They were chosen by Zheng Xian and Jaron. P.S.S. A googolplaxian is 10^googolplax. A googolplax is 10^googol. A Googol is 10^100. (100 is 10^2. 2 is 10^???.) P.S.S.S. The info in brackets are for dummies. P.S.S.S.S I did not really check it a googolplaxian times. It is like a metaphor. Rayner

Seriously, what the heck(please forgive me for using this word) is a P.S.S.? Illio

Misprint! I sp**o**tted a misprint in the puzzle. According to the point of view of Sheldon, the 483 should be 484. Then you just add a horizontal line above the 946 (or more informally, canceling the 1110110010 (B to D again!)) Jeremy

Jeremy, Rayner said in the discussion page that there should be no cancelling. Zheng Xian

Erm Rayner? is **1** considered a line? Yun Yee

From below to the line nearest to us, this comments are irrelevant. Zheng Xian

Should I write a googalplaxian for you? Wei Yang

PSS, PSSS, PSSSS? What is that? Anyway 2 is 10^0.301029995. And it should be googolpl**e**x and not googolpl**a**x. And a googolplex does not have enough room in the entire universe to write even if each digit was 10^30 smaller than an atom. Jeremy

It is a yes to YY's question There is NO MISPRINT! Rayner

There is enough space, in the internet! Wei Yang

Provided your computer was bigger than the universe. Ng Jian Rong

And There is no misprint, because this page wasn't even printed! WY

Ai Sp@ce, anyone? Jeremy (ß!)

Huh? What do you mean, Jeremy?

Please solve this question, if not you all give up then I will give the answer. Rayner

There is no misprint and there is a solution to the answer. P.S.The numbers 946,483 and 9684 were all chosen by others,not me Rayner

Ok, it has been ages. Rayner is not even IN this wiki anymore. Yet the answer is NOT revealed yet... I really would like to know. Alex

He is.

Yeah he is. Who wrote the previous post? Isaac

Me. I forgot to put my name. Zheng Xian

Hi. Does anyone wants to know the answer? Rayner

Actually, you all might have noticed the answer. You said that the 483 is supposed to be 484. So, ponder about it. Where is the extra one supposed to come from? Rayner

I know! Somehow we need to replace the 946 with a 1. Then it would be 1+483+9684=10168 and it will be correct. ~Isaac

Right! Isaac! You are on the right track! Just think about how a stroke and 946 can become the number 1. Rayner

Maybe you can get a very thick paint brush and some black paint and just paint the 1 right on top of the 946. The thick paint should cover the 946 totally. ~Isaac

What is 10+20-99/(divided) 1*(times) 3= Jarret

-23 Isaac

-267 Zheng Xian

-267 Rayner

-267 Yun Yee

You are all wrong, BODMAS rule makes you divide and multiply numbers before doing addition and subtraction, so: 10+20-99/1 x 3 = -69/3 = -23 Isaac

What are you doing?You did the addition and subtraction first! It should be: 10+20-99/1 x 3 =10+20-297 =30-297 =-267 Am I right? Rayner

Rayner should be right, that's how i worked it out. Yun Yee

If you want me to show you how I did it with my way, look: 10 + 20 - 99 / 1 x 3 = 10 + 20 - 99 / 3 = 10 + 20 - 33 = -3 Oops! I guess I was wrong too! so now -3 is my answer, Jarret. Isaac P.S. It is not 99 / 1 = 99 then x 3 = 297, Remember BODMAS?

According to my answer, you are all WRONG!!!!!!!!!!!!!!!!!!! I also used the BODMAS rule Isaac.. The answer should be -3237 I find this complicating too.... Explaination: 99 divided by 1= 99. 99 multplied by 33 is 3267 30-3267= -3237!!!!! (Jarret)

About you Issac.... You have been doing the correct method. Just that you were careless and mistook 33 for 3. That is the reason for your mistake, and the others followed suit. That is why. (JARRET)

JARRET!!!!!!!!!!!!!!!!!!!!!!!!!! It's your fault!!!!!!!!!!!!!!!!!!! ZHENG XIAN OK, I am going to stop all this! To Puzzle You:Find the prime factors of 1000!+1 right now! (Must be done by tomorrow.) Jeremy

Just to help you, 1000!+1= 402,387,260,077,093,773,543,702,433,923,003,985,719,374,864,210,714,632,543,799,910,429,938,512,398,629,020,592,044,208, 486,969,404,800,479,988,610,197,196,058,631,666,872,994,808,558,901,323,829,669,944,590,997,424,504,087,073,759,918,823, 627,727,188,732,519,779,505,950,995,276,120,874,975,462,497,043,601,418,278,094,646,496,291,056,393,887,437,886,487,337, 119,181,045,825,783,647,849,977,012,476,632,889,835,955,735,432,513,185,323,958,463,075,557,409,114,262,417,474,349,347, 553,428,646,576,611,667,797,396,668,820,291,207,379,143,853,719,588,249,808,126,867,838,374,559,731,746,136,085,379,534, 524,221,586,593,201,928,090,878,297,308,431,392,844,403,281,231,558,611,036,976,801,357,304,216,168,747,609,675,871,348, 312,025,478,589,320,767,169,132,448,426,236,131,412,508,780,208,000,261,683,151,027,341,827,977,704,784,635,868,170,164, 365,024,153,691,398,281,264,810,213,092,761,244,896,359,928,705,114,964,975,419,909,342,221,566,832,572,080,821,333,186, 116,811,553,615,836,546,984,046,708,975,602,900,950,537,616,475,847,728,421,889,679,646,244,945,160,765,353,408,198,901, 385,442,487,984,959,953,319,101,723,355,556,602,139,450,399,736,280,750,137,837,615,307,127,761,926,849,034,352,625,200, 015,888,535,147,331,611,702,103,968,175,921,510,907,788,019,393,178,114,194,545,257,223,865,541,461,062,892,187,960,223, 838,971,476,088,506,276,862,967,146,674,697,562,911,234,082,439,208,160,153,780,889,893,964,518,263,243,671,616,762,179, 168,909,779,911,903,754,031,274,622,289,988,005,195,444,414,282,012,187,361,745,992,642,956,581,746,628,302,955,570,299, 024,324,153,181,617,210,465,832,036,786,906,117,260,158,783,520,751,516,284,225,540,265,170,483,304,226,143,974,286,933, 061,690,897,968,482,590,125,458,327,168,226,458,066,526,769,958,652,682,272,807,075,781,391,858,178,889,652,208,164,348, 344,825,993,266,043,367,660,176,999,612,831,860,788,386,150,279,465,955,131,156,552,036,093,988,180,612,138,558,600,301, 435,694,527,224,206,344,631,797,460,594,682,573,103,790,084,024,432,438,465,657,245,014,402,821,885,252,470,935,190,620, 929,023,136,493,273,497,565,513,958,720,559,654,228,749,774,011,413,346,962,715,422,845,862,377,387,538,230,483,865,688, 976,461,927,383,814,900,140,767,310,446,640,259,899,490,222,221,765,904,339,901,886,018,566,526,485,061,799,702,356,193, 897,017,860,040,811,889,729,918,311,021,171,229,845,901,641,921,068,884,387,121,855,646,124,960,798,722,908,519,296,819, 372,388,642,614,839,657,382,291,123,125,024,186,649,353,143,970,137,428,531,926,649,875,337,218,940,694,281,434,118,520, 158,014,123,344,828,015,051,399,694,290,153,483,077,644,569,099,073,152,433,278,288,269,864,602,789,864,321,139,083,506, 217,095,002,597,389,863,554,277,196,742,822,248,757,586,765,752,344,220,207,573,630,569,498,825,087,968,928,162,753,848, 863,396,909,959,826,280,956,121,450,994,871,701,244,516,461,260,379,029,309,120,889,086,942,028,510,640,182,154,399,457, 156,805,941,872,748,998,094,254,742,173,582,401,063,677,404,595,741,785,160,829,230,135,358,081,840,096,996,372,524,230, 560,855,903,700,624,271,243,416,909,004,153,690,105,933,983,835,777,939,410,970,027,753,472,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,001 Zheng Xian

Jeremy, Maybe it's better if you ask in class, not post it on the wiki? And I'll try to work out the answer for u ok? *sigh* Yun Yee

Can you? Isaac

Anyway, I don't understand it, how did you arrive at -3237 Jarret? Isaac What he means is **10+20-99/1*3=?** Therefore,the answer is 10+20-99*3 =10+20-297 =30-297 =minus 267 (There was a bug that prevented me from inputting hyphens) Jeremy

Jeremy!!!!! It is 10+20-99/1*__33__=??????? NOT 10+20-99/1*3! Got it?? (JARRET)

You asked 10 + 20 - 99 / 1 x 3, not 10 + 20 - 99 / 1 x 33. You made a mistake, somehow... Isaac OK,if it is really 10+20-99/1*33,then OK. Then what he means is 10+20-99*33 =10+20-3267 =minus 3237 I agree. Jeremy

OK, even if it is 10 + 20 - 99 / 1 x 33, then I'll show it to everyone STEP BY STEP so you can understand: 1. Using BODMAS, we know we are supposed to use multiplication and division first, from left to right. So, the first sign of multiplication or division is ... division! (In ...- 99 / 1 x ...) Therefore, 99 / 1 is the first step we should do. 99 / 1 = 99. The question is reduced to this: 10 + 20 - 99 x 33. 2. Then, look to see whether there's anymore multiplication or division left. There is! 99 x 33 = 3267 so the sum is reduced to 10 + 20 - 3237. 3. After that, just add or subtract left to right. Answer is ..... -3237

Yes, I agree. Jarret and Jeremy are right. But, the problem is that Jarret put 10 + 20 - 99 / 1 x 3 in the original sum which made us think the answer was -267! And the trouble is that Jarret still has not admitted that he posted it wrongly! (Actually, sorry to all. My earlier answer to 10+20-99/1x3 was -23 and then -3 right? I now know it is wrong! OK, it is -267.) Isaac

Regarding that **big** number that Zheng Xian put... (Wikipedia: WTF? OMG! TMD TLA. __ARG__!) Jeremy

Which number is the odd one out for each set of numbers?

a) 999, 36, 121, 8836, 784 b) 5057, 79, 3239, 9796, 7426 Isaac

The number is-a)121 b)5057 Reason: They did not end with a non-prime number. From:Yu Jun

a) 999 Reason: It is not a square number. Correct! Isaac

b)79 Reason: It is a prime number. By using your method your answer is correct but I have another answer by using another method, can you find it? Isaac

Sheldon Are you sure? Double-check! If you are wrong, find the factors of the 10000th Fibonacci number. Jeremy

Do you even know the answer to that? Isaac Well, the first few Fibonacci numbers are 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946... Jeremy

I might be able to work out the Fibonacci number but, I would take a long time, and the 10000th Fibonacci number is OBVIOUSLY VERY TEDIOUS!!! Rayner

I found a dumb reason for b) 79 is not a 4-digit number Rayner

Complete the sequence. a) 4547, 4549, 4561, 4567, 4583, 4591, ? b) 26, 52, 156, 780, 1560, 4680, 23400, ? Isaac

a) 4598 Actually,from what I see from 'History',Yun Yee changed my answer :'46800' to ??? !!!!!!!! Not Fair! Rayner

WHAAAAAAT? But i didn't even use my account on that day! I checked history, and yes, I saw the change in history. But I was sick on that day and didn't even TOUCH the computer!!!! Yun Yee

Nope, it is wrong but quite close to the number that I am looking for. Look at the relationships between the first 6 numbers and find the next number in that pattern. Isaac :)

b) 46800 (23400x2) Mandy

Correct! The sequence is x2, x3, x5 repeated a few times. Isaac

a) 4609 (4591+10+8) Zheng Xian No, Zheng Xian, can't you see, they are all _ numbers! Isaac P.S. Work the blank out yourself, if I gave you the answer you would have know it by now.

a) 4597 Zheng Xian Yes!!!They are all prime //numbers,Isaac! Jeremy

You got it boy! It is a sequence of prime numbers! Great work Zheng Xian and Jeremy. Isaac Try continuing the sequence. Is 4501 a prime number? Jeremy

Strange. YY said it wasn't her, then who. Maybe she used the school's computer and forgotten to sign out (The day before). The next day, another person used the same computer and went into wikispaces. Rayner

My! What Is Going On? Jeremy//

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+21.......100= ????? (Jarret- This is very simple for most people) 1+100=101, 2+99=101, 3+98=101....*(times)50=5050! The anonymous guy who did the answer as above is WRONG! Sorry to disappoint that person... (Jarret)

1+100=101, 2+99=101, 3+98=101.........*(times) 49 + 50 = 4999 Yun Yee P.S. I was not the anonymous guy incase u think so.

But there are 100 numbers from 1 to 100, and in my math olympiad class I got 5050 too! (My teacher said that it was correct) Isaac P.S. I also wasn't the anonymous guy, but I am going to check the 'history' of this page and see who did that, back in a minute!

The anonymous guy is....... Yu Jun! But actually, Bryan did some changes to his answer but forgot to put down his name. Isaac

I know it's 5050, but then again, if Jarret says it's wrong, I've got to try to work it out smartly. =P

100 x (100+1) / 2 = 5050 Zheng Xian

Jarret, it should be 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+ .......+100= ????? Chan Jun Da

Chan Jun Da 1+99 2+98 3+97 4+96......49+51=100 49*100=4900 4900+50+100=5050 What about letter frequencies? Jeremy

Hey Jun Da! You gave the clue away! I missed out number '20'! So the answer is 5030. (Jarret)

What a trick. I couldn't spot that at first. Isaac

Huh. What a good trick question. I think it's ** __BECAUSE__ ** (for Isaac on nagging that I use 'shortcut') people usually get tired of reading the whole question, and since this question is SO common, we can do it straightaway, without even realizing that the number '20' is missing. Yun Yee

Luckily I didn't do the qn. Harish

I actually saw it. Don't you think writing all the way to 21 is quite suspicious? Rayner

What is the sum of all the interior angles of a 26 sided polygon? (There is a formula for the answer to this question, i do not want you to get the answer by drawing a 26 sided polygon) Chan Jun Da

I will put up the answer out on this coming Wednesday. Chan Jun Da The answer is 4320 degrees. Jeremy

The answer is 4320 degrees and the formula is: if x is the number of sides, the sum of all the angles is 180 x ( x - 2 ). Sheldon

Totally correct for both of you! The answer is 4320 degrees. Chan Jun Da

There are 2 children, named A and B. They are standing at both ends of a 100km road. A walks at a speed of 6 km/h, while B walks at 4km/h. (a) How long must they walk until they meet each other?? (b) If A brought along a dog, that moves at 10km/h. The dog starts with A, moves to B, then moves back to A, and keeps repeating this until A and B meet each other. How far did the dog walk?? (JARRET)

a) 10 hours later. b) The dog moved 100km. Chan Jun Da Duh!(Except for the 2nd qn.It was confusing me)

What is the 350th letter in this pattern ABBCCCDDDDEEEEE......? (once its 26 Zs, the next pattern will be 27 As) Chan Jun Da

Z. Using Gauss' method there are 351 numbers until the end of the 26 Zs so the 350th number is the 25th Z so it is still Z. Isaac

Quite True, please refer to me in class any day to find out if your answer is correct. Chan Jun Da

Can't you tell me whether it is correct now? Isaac

Yeah, why don't just type it out in the wikispace? Yun Yee

So is it correct or not? Isaac

X(any number)/(divided)0=Y What is Y? Chan Jun Da (This is a question which I learned the answer from overhearing my mother answering this question which my brother asked) Also by Chan Jun Da Y is __infinity__. Jeremy Jeremy, Good news, you got this all (i will tell you about this in class tomorrow(Thursday) as i am scared if they find out the answer from your answer) Chan Jun Da

0 or X itself. Isaac P.S. I'm not too sure. Isaac, good news, you did this question so correctly, the answer is NOT 0 or X.

I think Jeremy is correct, it __is__ infinity! Who is this done by? Chan Jun Da

Me.(Isaac)

Obviously. Scientific Calculators say it is a math error. Go try it yourself. Anyway, I heard Mdm Teo say it is dangerous to divide a number by 0. It is very tedious. Rayner (Mdm Teo: Oh dear, when did I say it's dangerous//?? Anyway, does anyone know what do we mean by infinity? Why does the calculator reflect an error?)

Well...when I put 0/0 into my calculator, it just shows the letter E. Jeremy

The word infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end" or "bigger than the biggest thing you can think of") which arise in philosophy, mathematics, and theology. Wei Yang

So Infinity is unlimited, but undefined. Just like lines, planes and points in WS 60. Go and look. Isaac//

How many __**3-digit**__ //numbers have// __**at least**__ //1 even number? (Tricky) Jun Da

There are 400 numbers with the hundreds digit even, and 250 of the remaining 500 with an even tens digit, and 125 of the remaining 250 with an even ones digit so when you add the numbers up you get 775 and that is my answer. Isaac

Correct!!! Jun Da//

What is ((2*5+7+8)square route)*2+3(square))/5 (SIMPLE!!!) Chan Jun Da

Um, shouldn't it be ((2*5+7+8)square root//)?? Isaac

Does it matter if you know what it already means? Jun Da

It means (sqrt(2*5+7+8))*2+(3^2)/5. This means it is (sqrt(10+7+8))*2+9/5 =(sqrt 25)*2+9/5 =5*2+9/5 =10+1.8 =__11.8__ Jeremy//

What is 11/2minus the dot? (Lame!!!) a) 53 b) 54 c) 56 d) 57 Please state if there is an error. Chan Jun Da

There __is__ an error. Isaac

Correct!!! Jun Da ` So, what is the answer? Jun Da

Well, 11/2 = 5.5. Removing the dot would leave 55. Alex

But why would you want to purposely make these questions like this? Isaac

Divide 88 by 2 (nonsensical question) Chan Jun Da

Either 0, 8 or 44. Isaac

Wrong!!! (still got a few) Jun Da

33? Tricia

Correct!!! Jun Da

So, does that mean the answers are 0, 8, 33 or 44? Alex (Since you said correct)

Dunno... Megan

You have been appearing lately in all of the questions from now onwards. Anyway, Alex, you are correct. Jun Da

Er, but Megan did not appear in the next question. Anyway, there are so many trick questions in this page... Isaac

What is 5+10+15+20+25+30+......+105? (simple) Jun Da

(I have to tell something to Isaac) refer to me in class Jun Da

1155 (Using Gauss Theorem- 10 pairs of 110 and 55 in the middle of the number series) Tricia (Duh!)

Yes, you are correct but can you stop using lingo. Jun Da

Fine, whatever. Tricia

There are 7 girls in a bus. each girl has 7 bags. Each bag has a big cat and 7 small cats. There is no bus driver. How many legs are there? Zhia Yang

Answer: 1582 legs Tricia

8 x 4 x 7 x 7 = 1582 Answer: 1582 legs Isaac

My Answer: 1582 legs Alex

8x4x7x7=1582 answer:1582 (easy)Harish

All of you are correct. Right Harish, it IS easy.

Wasn't this question asked by somebody on the radio? Megan

Isaac and Harish, I think you meant (7*2)+(7*7*8*4)=1582 Rayner

"What is the weight of this box of papayas?" asked the customer. "One eighth of its weight plus 28kg," answered the fruit seller. How heavy is the box of papayas? (Simple) Tricia

Oh, I know the answer. So since the total weight is one-eighth plus 28 kg, the 28 kg is seven-eighths! So, one eighth is 28/(divided by)7=4. Answer: 4+28=32 Statement: The box of papayas is 32 kg. Alex

Absolutely Correct!!!! Tricia

That is easy, the answer is 32 kg! Megan(obviously!)

Whatever, Megan. Plus, I've noticed you've kinda just join this space, what took you so long, snail??? Tricia (Mdm Teo: Whether Megan likes your teasing or not, I think it's not right to be insulting. Don't you think so, Tricia?)

3, 10, 31, 94, 283, ? Find the missing number (Again, simple!!!). Tricia

I know! 3+7=10 10+21=31 31+63=94 94+189=283 So, 7,21,63,189 are all multiples of 3. And It's three times of the previous number you multiplied with. (e.g. 7 X 3=21 21X3=63...) Answer: 189 X 3=567 283+567=850 Statement: The missing number is 850 From Alex

Correct!!! (Again) Tricia

This Is Easy 1x(times)2x2022020220202030303033030303x222939393944399393391229299999191102020233332229933838338382882832838283283xinfinityx0= Harish

0 Tricia 0 Isaac

0 Alex (of course, since the last number is 0)

0 Alicia

0 Megan

0(simple as ABC) Jun Da (For your information, infinity is NOT A NUMBER. If you don't believe, go check the internet.) So the truth is there is no answer as there is an error in your question.

Erm, I think that 0 is the answer. if infinity doesn't stand for anything, then treat it as nothing! Yun Yee

But if infinity is not a number and you put it in a question, you cannot treat it as nothing. It stands for something but it is not a number thats all. Example ORANGE*APPLE, you are not going to say 0 are you. It is still something so the answer is still error. Chan Jun Da

Yes but even if you treat infinity as a number, 0 follows and anything divided by 0 is 0 so there... Isaac

So is the answer 0? Yun Yee

I guess so Wei Yang

Look at 'X(any number)/(divided)0=Y What is Y?' question above by Jun Da and below somewhere and he will say that infinity is undefined. It's just like space. If you have a spaceship with unlimited petrol and it won't ever wear and tear, if you go in one direction and go forever! Maybe Infinity is there in life to explain things that cannot be counted because there are too many things. Why not ask Mdm Teo? She should know. Isaac

FYI space is not unlimited, but the universe will be growing at a much greater speed so yeah, maybe it will go on 4ever unless it crashes or becomes a satellite.

What is the formula for this pattern? (this should not be tough) 1,6,15,28,45...... (If there is an error, please report to me.)(There should not be an error so don't say the numbers are wrong as there is a formula, so if you think there really is no formula, please tell me as i have the answer.) Chan Jun Da

Heh, why has not anybody answered my question. It is not that difficult is it? Chan Jun Da

Didn't u give me this question to solve when we were in class???the formula has a few u's in it, isn't that true? Megan

Well, that was the formula written upside down. So it uses n not u. Isaac thought it was u also. Jun Da

Well since nobody knows the answer then I will tell the answer. It is n square+(n-1)*n. Jun Da

Answer: 1000010 (please do a little bit of binary-to-decimal conversion, again) Jeremy

Jeremy said 66 I know what is binary(Base 2) Rayner

Do you know this mind-reading math trick?try it one someone and say that u can read their mind! 1) Ask the person to Think of any 3-digit number that has digits that decrease in order (e.g:851)ask the person not to tell u the number. 2) ask him/her to reverse the order of the numbers( e.g: 158) 3) tell him/her to Minus off the second number from the first(e.g: 851-158=693)and tell the person to remember the difference.p.s:if the person don't know what u are talking about, simplify it!u know what i mean, don't u?... 4)ask him/her to tell u the number that is his/her ones digit of his/her remainder, and minus it off from 9, which is your tens digit always, no matter what number the person thinks of!Then that is your hundreds digit!!!!!(the person tells u his/her ones digit is e.g;3, so 9-3=6, so u tell the person his/her remainder is 693! OK finished. any questions????????????????if got, pls post below. thnks:) Megan

Very interesting. Nice.Well i used it on my father and again i got his number. Which is 198. The number is 321.(I don't know why he thought of such a wierd number) Jun Da

Funny, didn't you give this to me in class a long time ago, Megan??? I liked it though. Tricia (P.S. I hope you don't mind me insulting you, I just wanna have some fun)

I want to try explaining (for those who do not understand). Think of the number as abc (not a*b*c) a>c no matter what. So, c-a would be a negative, which mean you need to borrow 10 from the tens place. In the tens column, it would be b-(b-1), so the answer in the tens column __**must**__ be a 9. Rayner

7*3+3/4+7*0/0+infinity (obvious because i wrote the answer some where in this page.0 Jun Da

I cannot see the answer anywhere on the page. So, I guess the answer is infinity+21.75 Rayner

Well Rayner, you are wrong. Look at Hari's question. I wrote that infinity is not a number and so when it is placed in this __number__ sentence, it is an error. And whats more is that 0 cannot be divided by 0 so the answer is not defined. Jun Da

The answer is...undefined. Jeremy

Whatever Rayner

Jun Da, you meant Hari__//**sh**//__'s question. Rayner

What is 0.35+0.245-0.01+0.76-0.65 and round the number up to the nearest 3-digit number.(It means like example this number 0.35.This is not the answer.) Clue: 7410320 The numbers are jumbled up. Inside there, three of the numbers are in the answer and in that thing, between all the three numbers, the gap of all of them is the same. (even if you find the answer in the clue, the numbers are jumbled up also) Jun Da Totally SIMPLE!!!

I know!!! Answer: 0.70 Rayner

Correct!!!!! Jun Da

One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there? Written in invisible ink, try to find out the question and give me the answer. Wei Yang

The answer: 50 humans, 24 horses Reason: We need one of the coolest tools in mathematics to crack it. That is the fascinating world of **simultaneous equations**. Let a be the number of humans, b be the number of horses. We know that a human has 1 head and 2 legs and a horse has 1 head and 4 legs. The equations are therefore 2a+4b=196 (1), a+b=74 (2) Subtracting (2) from (1) twice, we have 2b=48 so b=24. From (2) we now know that a=50. Therefore there are 50 humans and 24 horses. Jeremy

Whoa smart! Wei Yang

You can actually use assumption (which is quite common for these types of questions). Rayner

What place in this world can have their temperatures Fahrenheit and Celsius equal? Yet another Invisible question. Wei Yang

This question is not related to Math! Isaac (Anyway I know how to read the invisible, you used ... well I won't tell everyone. So obvious :-) )

It is somewhere where it is -40 degrees both in celsius and fahrenheit. ( I used a converter) Jaron

But where in the world is that cold? Maybe somewhere in Antarctica? Isaac

Hey it is related to math because you need to do converting of Fahrenheit and Celsius. and I'm happy to say that you are both exactly correct!!!!!! Wei Yang

i noe how to read it but how do you write it? it says what place in this world can have their temperature Fahrenheit Calsius equal? Adric

oh just type in microsoft word, make it white then copy and paste WY

Every month, a girl gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had $6666 left. Assuming she only gets money by allowance, how much money does she earn every month? Have you found out how to see the invisible writing? Okay, if you really have no idea how to see the 'invisible' here is a clue: H_G_L_G_T Wei Yang

Answer: $2592 Zheng Xian

Wrong! Wei Yang

But I see Zheng Xian now knows how to read the "invisible". Wei Yang

Here's my answer.$2584 Isaac

I don't think this is a good question. When does she spend her money? Rayner

since no one can answer this question, I shall tell the answer: 2222. Wei Yang

How did you get it??? Can you kindly explain it to us? Isaac

There is something wrong here. She shud have $6666 left or spent 1/8 of the remaining money on toys Rayner

Please EXPLAIN to us! Isaac

Wei Yang please explain. ZX

Oh yeah Rayner was right, she has 6666 left.

Yeah me! Rayner

Who can tell me the 10 millionth Fibonacci Number? (It has 2,089,878 digits)

Jarret

I can type it out but i don't think mdm teo will like it Wei Yang

I agree Wei Yang, I should give you all the website then: [|HERE!] (This is a lot of numbers) Jarret

Hey! that was the website I went to!!! Wei Yang

A whopping lot of numbers, too big for the Big Number Scientific Calculator. The biggest number that the Big Number Scientific Calculator can handle is (10^1000000)-1. Try it out at http://alpertron.com.ar/BIGCALC.HTM Jeremy

Added 12/8/08: The link above was my first hyperlink, when I was in the era of factorization. Jeremy (ß!)

There are 9 vending machines containing cans of drinks numbered 1 to 9. Each can is supposed to weigh 500 grams. One day the manager found out that there was this vending machine containing cans of drinks that weigh 500.1 grams. Using a weighing machine and taking only one reading, how do you, the worker, find out which vending machine contains the cans of drinks that weigh 500.1 grams? Tricia

Take n cans from the machine that vends can n. Then put them all on the scale. If the cans were all equal, the reading would be 4500 grams. But there will be the .x at the end: .x means the overweight cans are from the machine that sells can x. Jeremy

This is a trick not a question. Take 9 x a number from 1-9. Then multiply the result by 12345679. See what happens. Adric

Nice Illio

I have a question:

What is

(x-a) x[times] (x-b) x (x-c) x .... x (x-y) x (x-z) = ?

There is an answer, although it might seem impossible.

Jaron

I can work out the answer for you. But I will need at most two months. Hint: when you multiply two binomials together (@a#b)(@c#d) the answer is (@a@c)+(@a#d)+(#b@c)+(#b#d) Jeremy

I don't know if that will give you the answer, but if you look at the question in a certain way without using any calculations but just looking at the letters, you will get the answer easily. It is simple, really. Jaron

I think the answer is 0. Why? Because you would reach a stage '(x - x)' which is 0 UNKNOWN TIMES 0 = 0 Lateef asked me this question before Lateef please answer. Rayner

Rayner, I think it was me who told you the answer and told you not to tell. Anyway, it is correct as anything times 0 gives 0. Jaron

No, Lateef told me on http://sg.geocities.com/p3_adventurous Rayner

There are 7 boys in a bus. Each boy has 7 backpacks. In each backpack, there are 7 big dogs. For every big dog there are 7 puppies. How many legs are there in the bus? (Mdm Teo: May I know who posted this question?)

Ans: 10990

Working: 7*2=14 (number of legs the boys have) 7*7=49 (number of bagpacks) 49*7=343 (number of big dogs) 343*4= 1372 (number of legs the big dogs have) 343*7= 2401 (number of puppies) 2401*4=9604 (number of legs puppies have) 14+1372+9604= 10990 Jarret

I know this is strange but look at History And I saw that the question was written by somebody in Mdm Teo's account and Jarret's reply was also written in Mdm Teo's account!!! Is Jarret a hacker? or maybe Mdm Teo did not log off the computer in whatever homeroom and Jarret used the computer? So many crazy ways Rayner

Mdm Teo: This question was originally posted in 'Math Challenge' and I cut and paste it here instead. No hackers here, don't worry. This page is for students, 'Math Challenge' is for me to post questions.

The Anonymous person is... Nicholas! Rayner

How can the group cross the bridge in 17 minutes?
 * A**
 * B**
 * C**
 * D**

By: Hari

I don't get it. WY

You didn't state how long each person takes to walk, how many people can cross the bridge at the same time, etc. Yun Yee Yeah. How? How? How?

Isaac (confused)

Be specific Hari!!! The only thing I know is that 4 people need to cross the bridge in 17 minutes!!! Gavin

OK, Hari said that when he copied the question here, some words were missing. So what's the REAL question, Hari? Isaac

A checkerboard is missing two of its squares. The lower left square and the upper right square are gone. That leaves 62 squares on the board. You are given 31 dominoes. Each domino is a rectangle that can cover exactly two squares on the checkerboard. Can you place all 31 dominoes on the checkerboard, so that all 62 squares are covered? By: Adric Pang

No matter how hard you try, it is impossible. It was found in a Murderous Maths book Rayner

Yes, but can u explain why?( i know the answer) Adric

For every black square you cover, you have to cover a white square. So, you will cover 30 black and 30 white squares. And you would be left with 2 black squares which obviously cannot be covered because you will need 2 more white squares Rayner

Correct!!! Adric

5 + 5 + 5 = 550 Add one stroke to make this statement true. Rayner

Add a stroke at the +, so it becomes 5+545=550 Adric

Correct Rayner

What two-digit number when squared and cubed gives all the numbers 0-9 without repetition? Rayner

Hello? Is anybody even looking at this question? It just takes a few trial and error. Rayner

Actually Wayne told me the answer in class. It is 69. 69 squared is 4761 69 cubed is 328509 Rayner (writting for Wayne)

Nice trick, Wei Yang. Illio

99 times table trick: this trick works for 11-99 x 99 when you multiply lets say 54 to 99, the first two digits will be the number -1, so it be 53 then the thrid number is 9 minus the 1st number, so 534* the fourth number is 9 minus the 2nd number, so 5346

Don't believe go check the calculator WY

A simplified way: 99 = 100 - 1 n * 99 = 100n + 100-n n = any number you can think of Rayner

You mean "third number" Illio

You were going to the Arts exhibition On your way, you saw 3 men going to the Music exhibition Each man has 3 wives Each wife has 3 cats Each cat has 3 rats How many legs were going to the Arts exhibition? Rayner

The answer is 456 (right?) Jarret

Wrong!!! Haha! This is easy! Very easy! Rayner

The answer is either 2, or unknown. 2 because obviously u have 2 legs. but since the men, wives, cats, and rats were ALL going to the music exhibition, only u went. unknown because there may be other people coming from other places and entrances. well pls reply Zhia yang ! = i dunno

You are correct!!! Either 2 or unknown Rayner

pee-wit-cisely!!! Gavin

Anyway, you are wrong. The answer is 0,0,0. Jeremy

"Pee-wit-cisely?" Illio

Did you know??? Whenever you multiply a power of n by another power of n, you get another power of n !!! n = ANY NUMBER Rayner

When you multiply two different powers of the same number, keep the number and add the value of the powers together. For example: 2^2 x 2^4 = 2^6 = 64 Proof: 2^2 x 2^4 = 4 x 16 = 64

When you add two different powers together, its a different story. For example: 2^2 + 2^4, can you say it is 2^6 = 64? No! Proof: 2^2 + 2^4 = 4 + 16 = 20

What Rayner said can be proved by this. Isaac

Thanks! Rayner

11 21 1211 111221 312211 13112221 1113213211 31131211131221 13211311123113112211

what is the pattern? Find out the next row.

Wei Yang

wait a sec, this question and the next is the same questions given on "WHY DIDN"T I THINK OF THAT" right? so easy this Q. first row there were two one so the next row is 2 one, and the next is 1 two and 1 one. the next row: 11131221133112132113212221, i think Adric

Adric is right, by the way, the next number is 3113112221232112111212211312113211, and the next is 1321132132111213122112311211222113111221131221. Jeremy (PS: Why are you bolding in all the words?)

Wait a minute, didn't this appear in the AMEC's Triangular Numbers Worksheet? Isaac

This is called the look-and-say sequence. Jeremy

**Over 90% of people get this answer wrong! Do this in your head only:** **Take 1000 and add 40 to it.** **Now add another 1000.** **Now add 30. Add another 1000.** **Now add 20.** **Now add another 1000. Now add 10.

WY

i did this in my head, dun worry. answer:4100 am i correct? Adric** 5000? Gavin'

lol even though i not author, i noe u are wrong. as it is 10,20,30,and 40 not 100,200,300 and 400. u got spunked!!! adric

oops, calculation error!! Gavin

Find the least possible number of fruits in the basket at first.(do not use guess n check pls) Adric**
 * 80% of the fruits in a basket are apples, and the rest are oranges. 28 apples and 2 oranges are removed and the remaining fruits are put into groups of 9 fruits. In each group of 9 fruits, there are 7 apples.


 * WHY ISNT ANYONE ANSWERING???****IS IT DIFFICULT???****TOO DIFFICULT???****adric**

I know the answer...

Take a as the number of groups. 4(2+2a) = 28+7a 8+8a=28+7a 8a=20+7a a=20 There are 20 groups.

Checking... 20x7+28=168 20x2+2=42 Correct! So, 168+42=210 and there are 210 fruits in the basket at first.

P.S. There is only 1 answer, so there is no need to put "least possible" in the question. Rayner

If 1=5, 2=10, 3=15, and 4=20, what does 5 equal to?(5=?) (rayner,do not answer this) Gavin

er.. either 25, or 1. adric

__The wait is over. The holidays start now.__ 537369

What do you mean?? And who wrote this? Isaac

Jeremy wrote that: J:5 E:3 R:7 M:6 Y:9 Illio

How to find out someone's birthday: And there you have it! Illio
 * 1) Ask him to take the month he was born in: Jan-1, Feb-2...
 * 2) Multiply by 5
 * 3) Add 6
 * 4) Multiply by 4
 * 5) Add 9
 * 6) Multiply by 5
 * 7) Add to the day he was born
 * 8) Ask him for the answer
 * 9) In your mind, subtract it by 165 and it will be the hundreds+days

Didn't you present it to us already? Isaac

Just in case some people want to know it. Illio

By the way: I apologize for all the stuff that I created on this page. And here is another trick: Jeremy
 * Ask your friend to think of a number.
 * Tell him to subtract 1.
 * Then he should multiply the resulting number by 2.
 * After that, he adds the original number, and calls it out.
 * You then add 2 and divide by 3.
 * The final total is the thought number.

Illio, you are doing the longer way. In your formula, you have to ask for the month (In Step 1) and the day (In Step 7), so what is the use of this formula? Rayner

Word riddle: A legal document about twisted mind is driven by natural forces. Illio

Why ain't anybody solving my quiz? Is it really that difficult? Illio

WHAT? Jeremy

If no one is going to try to solve it regardless right or wrong, I will give the answers. Illio

What is the riddle about? Isaac

Word riddle. Let me give you a hint: Wind Illio

WINDMILL lol guessing. Adric

How did you know!!!!!!! Illio, I know why.A legal document is a will Twisted mind: MIND- NDMI

So, Will plus Ndmi = WIndmiLL Rayner

A man who went to visit a friend was turned away by his mother. His mother said:" No, you must have the wrong house. I'm all here on my own. That's why I didn't here your first ring." Sounds innocent enough, he was going to leave when he thought about what the mother said and approached the house again. Illio
 * What is wrong?**

Why ain't anybody solving my quiz? Is it really that difficult? Illio

Yes, it is really that difficult. Jeremy

If no one is going to try to solve it regardless right or wrong, I will give the answers. Illio

Interesting! Isaac ERM... i think i know.how did the mother know about the first ring if she did not hear it?Adric

Adric, you are totally correct!! Illio

This is NOT RELATED TO MATHS! And wasant this asked by someone on the radio? zHIA yANG

__A trick for quick multiplying of 11__

When you want to multiply a two-digit number by 11, for example 35, just add 3 + 5 and put the answer between the numbers! So, 3 + 5 = 8, and hence, 35 x 11 = 385! If let say you have 86 x 11, add 8 and 6 and you get 14. Do you put the answer as 8146? No! Carry the ten over to the hundreds place! 8 + 1 = 9 and the answer is 946!

So...... 27 x 11 = 297 51 x 11 = 561 67 x 11 = 737 93 x 11 = 1023

You can prove this with a calculator if you don't believe me...

Part 2: Algebra The formula for (with ab being a two digit number where ab = a x 10 + b) questions like ab x 11 is: a + b = c, Answer for question = acb (where the letters represent the digits of a three digit number)

Isaac

interesting adric

I noe that trick! Illio My father

Who told you? I learnt it from a Math 'Magic' Book, which has lots of techniques on how to multiply numbers ending with 5, square numbers and so on. Hey, teach you another trick. How to square a two digit number FAST? Come and learn!
 * __Square Squares__**

Say you have 37 squared. First, notice that 37 square is 37 x 37. Next, is 37 near any number with a zero at the end? Yup, 40! OK so we round the fir s t number up by 3 numbers to 40. So now the equation is: 40 x 37. Now, by how much did you round up? 40 - 3 = 37, so you rounded up by 3. How's the 3 useful? You may ask. Next, subtract 3 from the second constant in the equation. So 37 - 3 = 34, and the question becomes 40 x 34. Then again, how much did you round up? 3 right? Add 3 squared to the product of 40 x 34 and there's your answer.

40 x 34 = 1360 1360 + 3^2 (which is 9) = 1369 = 37^2!!

Don't believe me, ask a calculator! You can also round down instead of up, but you still add the square of the difference.

Here's a few more examples: 62 squared = 60 x 64 + 2^2 = 3840 + 4 = 3844 86 squared = 90 x 82 + 4^2 = 7380 + 16 = 7396 28 squared = 30 x 26 + 2^2 = 780 + 4 = 784

This is what I love: How do we find the square of a number ending with '5'? Simple! First, notice these: 1. The answer begins by multiplying the first digit by the next higher digit. 2. The answer ends with a '25'.

So, for example we have a lovely number 35 to square.Simply multiply the first digit (3) with the next higher number (4) first. 3 x 4 = 12. Then attach 25 at the back. And the answer is... (Drumroll) ... 1225! Cute eh?

More examples: 85 squared = 8 x 9 = 72, Answer is 7225 65 squared = 6 x 7 = 42, Answer is 4225

The beauty of mathematics in life is that there are two methods of doing things, the HARD way and the SHORTCUT way. Who says life has no shortcuts?

Isaac

P.S. If you want more techniques from me, just tell me either in class or here. But it would take up too much space. aybe Mdm Teo can allow me to create a new page specially for my techniques...

I already know this! Jeremy

Good! Want more? Isaac

Yeah! (Nice) Illio

Trick #4: **Super Prediction and Addition**

If let's say a daring friend challenges you to find the sum of 10 numbers following the Fibonacci pattern (1st no. + 2nd no. = 3rd no. and so on), you can compute the sum even before he finishes writing the numbers! Example: Find 9 + 5 + 14 + 19 + 33 + 52 + 85 + 137 + 222 + 359. (If you use a calculator or your brain you will get 935) But the trick of fast adding is... Multiply the 7th term by 11. So, the 7th term in the example is 85, and 85 x 11 = (using the method that I taught you above) 935! Try this with other numbers if you don't believe me.

I can explain. Take the 1st number as x and the 2nd number as y.

As you can see the 7th term is 5x+8y and the total is 55x+88y. 11(5x+8y) is 55x+88y, so it is proved. Actually, you can multiply the first number multiply by (5*11) and add the answer to the second number multiplied by (8*11). It might be faster. Rayner
 * 1st number || x ||  ||   ||
 * 2nd number ||  ||   || y ||
 * 3rd number || x || + || y ||
 * 4th number || x || + || 2y ||
 * 5th number || 2x || + || 3y ||
 * 6th number || 3x || + || 5y ||
 * 7th number || 5x || + || 8y ||
 * 8th number || 8x || + || 13y ||
 * 9th number || 13x || + || 21y ||
 * 10th number || 21x || + || 34y ||
 * Total || 55x || + || 88y ||

Trick #5: **A Day for Any Date** Want to find out the day of the week of your common test? Your doctor's appointment? This nifty little algorithm will help you find out!

Step 1: Pick numbers for the date (1-31), month (1-12) and year (e.g. 2003) you want to find out. Step 2: Another variable in this equation is f//. If the day you are working out is in January or February, the value of// f //is 1. Otherwise// f //will be 0. Step 3:// y = year - f //Step 4:// m = month + //12//f - //2 Step 5: Got all the variables already? If yes, insert the values into the formula below: (the '/' sign means divided by) (//date + y + //[31//m///12] + [//y///4] - [//y///100] + [//y///400]) MOD7 MOD means that you divide the whole thing by the number after the mod (in this case, 7), and take the remainder. Don't care about the quotient, just find the remainder. Cut away all decimals from the answer and make it a round number, but only round down, not up. E.g. if you get 4.82, the answer you take in is 4. Step 6: Convert to the day of the week: 0 = Sunday 1 = Monday 2 = Tuesday 3 = Wednesday 4 = Thursday 5 = Friday 6 = Saturday Done! Let's try an example, Christmas this year (25 Dec 2009). The calendar says that it is on a Friday, so we are going to test if the formula works. So, f = 0 since the month is December. y = 2009 since 2009 - 0 is still 2009. m = 12 + 0 - 2 = 10 Put the values into the formula: 25 + 2009 + (31 x 10 / 12) + (2009 / 4) - (2009 / 100) + (2009 / 400) = 25 + 2009 + 25 + 502 - 20 + 5 = 2546

Divide 2546 by 7 and the remainder is 5. Look at the table and 5 is for Friday. There! That is the same as the calendar so it's proof that the algorithm works. If you have lots of time to waste, you can check for the whole class which day is their birthdays. Well, I do, so I will list down ALL birthday days for Int/Adv students in P4. Met/Res, get somebody to work it out for you...

Alicia - 8 May - Friday, Megan - 19 Jul - Sun, Michelle - 23 Nov - Mon, Zhi Rui - 10 Feb - Tue, Yun Yee - 19 Apr - Sun, Tricia - 25 Mar - Wed, Kai Ren - 19 Jun - Fri, Jun Da - 26 Apr - Sun, Bill - 31 Mar - Tue, Gavin - 9 Jan - Fri, Jian Rong - 16 Nov - Mon, Adric - 29 May - Fri, Ronald - 29 Dec - Tue, Sarthak - 20 May - Wed, Yu Jun - 24 Jun - Wed, Hari - 10 Jul - Fri, Huang Zhong - 31 Dec - Thu, Illio - 6 Aug - Thu, Jeremy - 4 Dec - Fri, Javier - 22 Dec - Tue, Bryan - 8 Aug - Sat, Isaac - 19 Aug - Wed, Timothy - 25 Feb - Wed, Zhi Yuan - 29 Oct - Thu

Sunday - 3 Monday - 2 Tuesday - 4 Wednesday - 5 Thursday - 3 Friday - 6 Saturday - 1

Done! Isaac

WHAT??? Jeremy

Never mind.

Can you draw a table It is very confusing. Rayner (table below is by me)// Sun-2 Mon-5 Tue-3 Wed-2 Thu-4 Fri-4 Sat-5 ---//---
 * Mandy || 2 Feb || Mon ||
 * Doreen || 29 Jul || Wed ||
 * Kong Yann || 13 Jul || Mon ||
 * Shannon || 3 Jul || Fri ||
 * Cheri || 2 Jan || Fri ||
 * Anushree || 21 Dec || Mon ||
 * Ee Sing || ??? || ??? ||
 * Lateef || 20 Mar || Fri ||
 * Alex || 4 Apr || Sat ||
 * Harish || 9 Nov || Mon ||
 * Po Chun || 14 Mar || Sat ||
 * Geng Leong || 21 Jul || Tue ||
 * Rayner (me!!!) || 15 Sep || Tue ||
 * Jaron || 6 Jun || Sat ||
 * Zheng Xian || 14 May || Thu ||
 * Mudzakkir || 1 Oct || Thu ||
 * Farhan || 22 Jan || Thu ||
 * Ilyasaq || 26 Jun || Fri ||
 * Jarret || 11 Jan || Sun ||
 * Neville || 11 Mar || Wed ||
 * Zhia Yang || 15 Dec || Tue ||
 * Sheldon || 21 Mar || Sat ||
 * Shivanand || 12 Apr || Sun ||
 * Kheng Hun || 26 Mar || Thu ||
 * Wei Yang || 11 Apr || Sat ||
 * Wayne || 25 May || Mon ||

OK, my first trick only showed you how to find the product if you multiply a two-digit number by 11. This trick will show you a method for ALL numbers, however long or short it might be.
 * Trick #6: Another trick for Multiplying by 11, this time for ANY number!!**

Example: Find 24136 x 11 (in 6 seconds) 1...2...3...4...5...6 Time's up! Did you get 265496? If not, or even if you did, but with the normal working or with a calculator, look below... To multiplpy 24136 by 11, first copy the first number (which is 2) down: 2 Then, add the first number to the second number and write the result down: 26 Then, add the second number to the third number and write the result down: 265 Then, add the third number to the fourth number and write the result down: 2654 Then, add the fourth number to the fifth (also the last) number and write the result down: 26549 Lastly, copy down the last number: 265496. See, done! If the sum is more than ten, carry the ten over to the next place and add 1 to it.

Isaac (from Glad2teach.com)//

The Easy Way of Multiplying 4294967296 By 262144 By Jeremy

First, you need to know about the UT method. Example: What is the UT of 59*6? 5. Why? U T 5 9 * 6 3__0 5__4 0+5=5 In general: multiply each of the two digits of the first number by the second number, and take the units of the tens product and the tens of the units product and add them together.

Now we come to terms with the multiplication.

0 0 0 0 0 0 4 2 9 4 9 6 7 2 9 6 0 * 2 6 2 1 4 4 ........................................... answer is written here (The last 0 in the long multiplicand is just to clarify the method.)

First, find the UT product of the last two digits of the long multiplicand by the last digit of the short multiplicand, and place it under the first digit of the long multiplicand: 2__4 0__0 =4 so: 0 0 0 0 0 0 4 2 9 4 9 6 7 2 9 6 0 * 2 6 2 1 4 4 ........................................... 4

Now we shift the original digit one place to the left and introduce the second digit: 3__6 2__4, 2__4 0__0 =12 so: 0 0 0 0 0 0 4 2 9 4 9 6 7 2 9 6 0 * 2 6 2 1 4 4 ............................................. 2 4 and then we repeat this process.

Challenge: with this method (and no calculators), can you do this multiplication?

Um Jeremy, what is UT?

UT stands for **u**nits-and-**t**ens product. Jeremy

But I still can't understand it. Can you explain it to us slowly? Isaac

It takes an hour for a man to dig a hole. How long does it take for 3 men to dig 3 holes? Illio

omg this is so easy 1 minute lah!YY

wrong^^ u r so careless it is 1 hour lah Illio

1 hour! If it is so easy, then why did you get it wrong??? Isaac (sorry I deleted your post accidentally, Illio)

oops careless mistake (as usual....) sry read the thing wrongly, i meant 1 minute ^_^YY

Ha, you STILL got it wrong! Isaac (my my you must be real careless (no offence))

..... dont worry im not the sensitive type. ok now its 1 hour ok i got it right finally..... YY

Three hard questions for you: 1. If Papa Rabbit can dig a hole in 4 1/2 minutes, Mama Rabbit can dig the same hole in 6 minutes and Baby Rabbit can do it in 9 minutes, how long will it take the three of them to dig the hole at the same time?

2. Bob loves to drink iced tea. At a supermarket, he can exchange 5 empty bottles for a full bottle of iced tea. If he has 77 empty bottles, how many bottles of iced tea can he drink altogether?

3. Susan has only 50-cent coins whereas Tina has only 20-cent coins. If Tina has 19 more coins than Susan and Susan has $1.30 more than Tina, how many 50-cent coins does Susan have? If you can answer them you are a maths genius(please show the working)! Illio

Answers: 1. 2 minutes. If Papa Rabbit can dig a hole in 4 1/2 minutes, each minute he can dig 2/9 of a hole. If Mama Rabbit can dig a hole in 6 minutesm each minute she can dig 1/6 of a hole. If Baby Rabbit can dig 1 hole in 9 minutes, he can dig 1/9 of a hole in one minute. Add them together, and you find that 2/9 + 1/6 + 1/9 = 1/2. So, if all of them can dig 1/2 a hole in one minute, to dig one hole will take 1/0.5 = 2 minutes. 2. 19 bottles. 15 + 3 + 1 = 19. 3. OK, am I a math genius? The answer is 17 20-cent coins. Working below: We must find what is the total value of the 19 more coins that Tina had. 19 x 0.2 = 3.80 Then, add $1.30 to $3.80. 1.30 + 3.80 = 5.10 Divide 5.10 by the difference between the values of the two coins. 5.10 / 0.30 = 17 (Answer!)

Isaac (working included now!)

The Proof that **Any Number** = 0 1 + 1 =1 + square root of 1 =1 + square root of (1 squared) =1 + square root of (-1 squared) =1 + (square root of -1) squared =1 + **i** squared =1 + (-1) =0

Since 1 + 1 = 0: 2 = 0 Divide by 2: 1 = 0

We can multiply the equation by any number to get: QED.** Jeremy
 * any number = 0

Hey! How can square root of (-1^2) = (square root of 1)^2?? Anyway, QED means 'that was to be demonstrated'.

I have another piece of proof that any number = 0. Watch: Pick any two numbers that are the same. We call them a and b. If a and b are the same, we can write: a=b. Multiply both sides by a: a^2 = ab Subtract b^2 from both sides: a^2-b^2 = ab - b^2 a^2 - b^2 can be written as (a - b)(a + b) also. The other side, ab - b^2 can be factorized to become b(a - b) So, the equation becomes: (a - b)(a + b) = b(a - b) Divide both sides by (a - b): (a + b) = b Open up the bracket: a + b = b Subtract b from both sides: a + b - b = b - b And so...: a = 0

Well, a could be anything, so I have therefore proven that any number equals to 0. Of course that's rubbish, every number cannot equal to 0. So what did I do wrong?

Isaac

Addendum: **Any Number = Any Nunber** Remember the above proof? To get x = y, we make (x - y) = 0, and then add y: QED.** Jeremy (1 * 1 = -1 * -1)
 * x = y

I know why it is wrong. Since a=b, a-b is 0, and you cannot divide anything by 0 Rayner

What is the SQRT of i? Zheng Xian

The square root of i is plus or minus the square root of 2 divided by 2 multiplied by one plus //i//. Jeremy

Ans: So you are wrong. Zheng Xian

Am I wrong? //My// answer is correct! Jeremy

It's //wrong//! Zheng Xian

I accept it, now, what is the square root of //-i//? Jeremy

There is no such thing as -i. Zheng Xian

There //is//. //i// multiplied by //i// multiplied by //i// is equal to (-1) multiplied by //i// is equal to //-i//. Jeremy

i is just an imaginary number and so you can't have something like -i. Zheng Xian

There are 2 square roots of i: and. (gotten from []) So is your dispute finished??

And I agree with Zheng Xian that there is no such thing as -i. Remember i x i = -1 and both 'i's are equal. can you find two exact numbers that multiply together to make -1, or any negative number, for that matter?? Isaac

If square root of -1 = i, then you can deduce that i squared is -1. So i times i = -1. We don't know if this imaginary number is positive or negative, because positive multiplied by positive is positive, positive multiplied by negative is negative, negative multiplied by positive is negative, negative multiplied by negative is positive. So how can negative multiplied by negative equal to a negative number? Anyway when I key in square root of -1 in the calculator, the calculator responded with Math Error. Isaac

(Mdm Teo: Please do not use offensive and insulting language in my wikispace. Please contribute relevant comments on Math. Anyone who breaks this rule will be barred from remaining in the wikispace for a period of time.)

If i is positive, the sqrt of -i is i*(sqrt i), right? Anyway, I can prove Zheng Xian answer. He said that: And here is the proof: Also, here are the cube, fourth and fifth root of i (if you want them): The fifth root of i might be strange but i^5 is i(i*i)(i*i) = i*-1*-1 = i*1 = i Rayner

Message #1 OFGHBEPTCXW5QAJAK32BKKLBFTKETZTXSBRSYGAP Jeremy

Why is nobody responding? Jeremy

OK let me show you that every number is undefined.

You know that if a x b = c, then c / b = a and c / a = b. For example, 2 x 3 = 6, than 6 / 3 = 2 and 6 / 2 = 3

Now, take 5 x 0 = 0. If you reverse it, it becomes 0 / 0 = 5. But 0 divided by 0 is undefined, so 5 = undefined. Substitute 5 with any number and it will work! Everything has become undefined!

Isaac

Does anyone know why 0 to the power of 0 is Math Error (based on calculator), not 1?

Isaac

For all x, x^0 = 1 so 0^0 = 1. For all x, 0^x = 0 so 0^0 = 0. Therefore 0^0 = Math Error. Jeremy

Message #2 I 7377662559 2354383 THAT THE RIEMANN HYPOTHESIS IS TRUE. I HAVE A PIECE OF PAPER TO PROVE IT. OVER 150 YEARS OF 28836787 ARE ABOUT TO BE ENDED BECAUSE OF ME. Jeremy

I don't know anything about this. Isaac

I've pieced most of the message together above. Remember the handphone code, Isaac. Jeremy

What is the area of a triangle with sides 5cm, 5cm and 10cm? (from Farhan) Isaac

It is not possible to create such a triangle as mathematically speaking, quoting from Euclid "The shortest shortest distance between any two points is a straight line"

Kheng Hun.

I agree with Kheng Hun. Using that Pythagoras theorem, you can figure it is impossible. 5^2+5^2=25+25=50 Rayner

What number is the sum of the factorials of its digits? For example, the number is abc (not a*b*c) and abc = a! +b! +c!. Rayner

1, 2

I think there may be other answers but I cannot think of any others yet. Kheng Hun

Okay, other than 1 and 2. Rayner

The answer is...40585? Zheng Xian

Yes! Rayner

If 24,678,050 = 2^8 + 4^8 + 6^8 + 7^8 + 8^8 + 0^8 + 5^8 + 0^8, find another 8-digit number which is also the sum of the 8th powers of its digits (This should be simpler than the one about factorials). Rayner

Complete the pattern: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, _, _, _... Rayner

(not drawn to scale)

BC=BD AC=3AF ABD has an area of 48cm² So, what is the area of AEF? Rayner

How can BC=BD? Kheng Hun

Hello? Were you paying attention? I already said that the diagram was not drawn to scale! Rayner

a) How many numbers from 1 to 1000 can be formed by the difference of **__the square root of two square numbers__**? b) How many numbers from 1 to 1000 can be formed by the difference of __**two square numbers**__?

This might be a little tricky. Rayner

What is a^3 - b^3? Write in terms of a and b. Rayner