Archive+Puzzles+1+to+20

Question 20 - Mrs Lim In 2005, both John and Mary have the same amount of pocket money per month. In 2006, John had an increase of 10% and Mary had a decrease of 10% in their pocket money. In 2007, John had a decrease of 10% and Mary an increase of 10% in their pocket money. Which one of the following statements in correct? (a) Both have the same amount of pocket money now. (b) John has more pocket money now. (c) Mary had more pocket money now. (d) It is impossible to tell who has more pocket money now. (2007 Math Olympiad)

Solution 20:

John=J Mary=M Year: John's money Mary's money

2005: J=M 2006(if M=J): 1.1 J, 0.9 J 2007: 1.01 J, 0.99 J

Ans: (a) False (b) True (c) False (d) False

So the answer is (b)! case closed~Alex

Sorry Alex, you've made a computation error in line 2007: 1.01J, 0.99J, so your final answer is incorrect. ~ Mrs Lim

If John and Mary have each $100 at first, 2005: John=$100 Mary=$100 2006: John=$110(100+10) Mary=$90(100-10) 2007: John=$99(110-11) Mary=$99(90+9)

So the answer is (a)!~Yi Rui

Hurray! Using a nice value such as 100 helps to make the problem easier to solve. Good job, Yi Rui! ~Mrs Lim

Question 19 - Mrs Lim

In a social gathering, each of the 38 boys talked to 3 girls while each girl talked to 2 boys. Find the number of girls in the social gathering. (2006 Math Olympiad)

Solution 19:

There were 57 girls~ Garett Correct! Can you provide some explanation how you arrive at 57? ~ Mrs Lim In that particular social gathering, we can say that every 2 boys talked to 3 girls so the ratio of the boys is to girls is 2:3 so 38 divided by 2 times 3 is equal to 57. Yup, this is one way of getting the answer. ~ Mrs Lim



Question 18 - Mrs Lim

In a party, there is a group of children. The boys always lie and the girls never lie. 10 children make the following statements A: Only one of us is a boy. B: Only two of us are boys. C: Only three of us are boys. D: Only four of us are boys. E: Only five of us are boys. F: Only six of us are boys. G: Only seven of us are boys. H: Only eight of us are boys. I: Only nine of us are boys. J: All of us are boys.

Which of them is/are girl(s)? (2006 Math Olympiad)

Solution 18: Only I is a girl.~ Wan Cheng Fantastic! How did you reason this out? ~ Mrs Lim

Because J cant be telling the truth as he would be lying if so. if A tells the truth, everyone else is lying, which makes him to be lying, thus making him a boy. and so on with B, C, D..... if we continue, we find only I tells the truth.~Wan Cheng

All the options are put in such a way that there could only be 1 girl. For example if A and B are girls then at least one of them must be lying because their options contradict each other so there is only 1 girl. Since there is only 1 girl, there would be 9 boys( unless an alien comes and made one of the boys bisexual...). Since I said there was 9 boys so i must be telling the truth and she must be a girl!~Alex

Question 17 - Mrs Lim A family consists of 1 grandfather, 2 fathers, 1 father-in-law, 1 brother, 2 sons, 1 grandmother, 2 mothers, 1 mother-in-law, 1 daughter-in-law, 2 sisters, 2 daughters, 4 children and 3 grandchildren. What is the smallest possible number of persons in this family? Who are they? (2007 Math Olympiad)

Solution 17: 7 people. They are the grandfather(also the father of a son), the grandmother(also the mother of the same son) the son's wife, the son, 2 grand-daughters, and a grandson.~garett Fantastic! I've been waiting for someone to arrive at an answer. ~ Mrs Lim

Question 16 - Mrs Lim  Find the number of ways to put 4 different coloured marbles into 4 identical empty boxes. (2007 Math Olympiad)

Solution 16:

Is it a must to fill up every box?~ Garett 121 ways~ Yi Rui There are only 4 marbles. Try to make a table to work out this one. ~ Mrs Lim If it is a must to fill up every box then it's 24. Otherwise it's 4x4x4x4=256.~Alex The 4 boxes are identical, that is, it makes no difference whether you put ball A into box 1 or 2 or 3 or 4. ~ Mrs Lim



Question 15 - by Garett

Timid Tommy tumbled upon a field containing twenty-two tomatoes. How many 't's are there in that sentence? 7??? ~ LBQ 5 "t"s and 2 "T"s ~ WeiC Or 3 't's in "that sentence" ~ WeiC ...and two 't's in ''t's are there' ~Daniel Congraulations WeiC for getting it correct.(for his second answer, that is.) There are 9 "t"s and "T"s

Question 14- by gerry

Here's some crazy sums to start you off: 1) //Let S be a subset of the set of numbers {1, 2, 3, …, 2008] which consists of 756 distinct numbers. Show that there are two distinct elements a, b of S such that a + b is divisible by 8.( Know your pigeonhole principle first)//

2) Let //m// and //n// be integers greater than 1. Consider an //m// x //n// rectangular grid of points in the plane. Some //k// of these points are coloured red in such a way that no three red points are the vertices of a right-angled triangle two of whose sides are parallel to the sides of the grid. Determine the greatest possible value of //k//.

3) Every day the seven dwarfs set off to work in a line. Every dwarf is a different height, and they always arrange themselves so that each dwarf is either at one end of the line, or between two dwarfs who are both taller than him, or between two dwarfs who are both shorter than him. That means that if you look along the line of dwarfs your eyes will either go up-down-up-down-up-down, or down-up-down-up-down-up.

The question is this: if each day they set off in a different arrangement, for how many days can they go to work without repeating any arrangement?

4)//The number 916238457 is an example of a nine-digit number which contains the digits 1 to 9 exactly once. It also has the property that the digits 1 to 5 occur in their natural order, while the digits 1 to 6 do not. How many such numbers are there?

5)////Three consecutive even numbers are such that the sum of four times the smallest and twice the largest exceeds three times the second by 2006. What is the sum of the digits of the smallest number?//

6a) Nine schoolgirls go for a walk every day. They walk in groups of three abreast. Show how they can do this for four days so that no two girls are in the same group of three more than once. b)The nine schoolgirls are joined by six more, making fifteen altogether. Is it possible for them to walk in groups of three every day for a week so that no two girls are in the same group of three more than once?  Here are some harder ones: 1) //Beth rides to her friend’s house at 30 kilometers per hour and back again at 20 kilometers per hour. What is her average speed?// ( It is NOT 25 kilometers per hour!)

2) //Let N be the smallest integer such that 10 x N is a perfect square and 6 x N is a perfect cube. How many positive factors does N have?//  3) //Inzamam runs twice as fast as he walks. On Monday, when going to school, he walked for twice the time for which he ran. On Tuesday, doing the same journey, he ran for twice the time that he walked and was six minutes quicker than on Monday. On Wednesday, he walked all the way to school. How long did it take him?//

4)John can't be bothered to match up his socks by colour in pairs and instead he mixes up his 5 pairs of black socks, 10 pairs of brown socks and 15 pairs of grey socks in a box. Tomorrow John is going on a school trip for a week. What is the smallest number of socks he needs to take out to guarantee that he will have at least 7 pairs of socks of the same colour?

5) If x = 12 + 22 + 32 + ... + 20052 and y = 1 x 3 + 2 x 4 + 3 x 5 + ... + 2004 x 2006,

what is the value of x - y? (Attempt if u are good with algebra.)

//Happy bashing your heads on the wall for answers!!!! =)//

Solution 14 Gerry, for your question 2 in your 'harder ones', the answer is 1 (the answer is 0) -Daniel 0 is NOT a cube and it is also NOT a square. (I think... Go check it out) - Gerry YES it is. Try it with your calculator. Put square root 0=0. Cube root 0=0

Whether 0 is a square number depends on how you interpret it. Refer to this website for some explanations: ~ Mrs Lim []

Also 0x0=0 and 0x0x0=0. Right? So 0 IS a square and IS also a cube The answer for number 2 in harder ones is infinity!!! 6 x 0 = 0 and 10 x 0 = 0... 0 is the square and cube of 0. It is infinity because 0 x 1 = 0, 0 x 2 = 0, 0 x 3 = 0, 0 x 4 = 0,0 x 5 = 0, etc. all the way to infinity ~ LBQ Err... LBQ, I do not think that the answer is infinity because Gerry said that there is a proper answer (besides 0 that is) -Daniel The answer for Q3 in harder ones is 36 mins. 6 mins is how long Inzamam taks to run one third of the journey. To run the whole way would take him 6 x 3 = 18 mins He would take twice the time to walk so he would take 18 x 2 = __36 mins__. Right??? ~ LBQ 18 x 2 = 32?????? LBQ, you should really check your answers for careless mistakes. And Daniel, you answers are correct. Good Job! =) - Gerry Even though my answer is correct, what is the REAL answer??? ~Daniel I mean check out whether 0 is a square and a cube on google, yahoo, yahooligans...etc. - Gerry Ok. Check this out: [] and this too: [] for perfect squares Can somebody at least try to answer any one of the question??? - Gerry I think LBQ meant 36~ Garett I think the answer for number one of your harder questions is 30km/h~ Garett Sorry but your answer is wrong Garett - Gerry Is it 24km/h? (for the 1st of your harder questions, and Garret spelt 'harder' wrongly) ~Daniel For your 4th harder questions, is the answer 14? ~Daniel Sorry, I changed my answer. Is it 36? ~Daniel To Gerry Zhang: Q1 for the harder parts is impossible w/o time taken. 75181825 919 914 1215225 239208 51391225  <span style="color: rgb(244, 31, 31);">NO I AM NOT U 11919815125 <span class="content" style="color: rgb(0, 0, 0);"> Q1 in harder ones is 24km/h. The ratio of the time Beth travls 20 km/h to the time that she travels 30 km/h is 3:2, so... 20 x 3 + 30 x 2 = 120 and 120 / ( 2 + 3 ) = 120 / 5 = __24 km/h__ ~ LBQ Q6A- 1st day-ABC DEF GHJ 2nd day-ABD CEG FHJ 3rd day-ABE CFG DHJ 4th day-ABF CEJ DHG I omitted i because it's confused with 1.

Q6B-Impossible.

Question 13 by Jeremy Does anyone know what is the //volume// of the singularity in the smallest possible black hole (assuming that there is no Hawking Radiation)? P.S. it is not infinity. The volume //can// be calculated, but not the density

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">SolutioN 13 If you want the answer, press Ctrl and A at the same time,or select all from the right-click control panel. <span style="color: rgb(255, 255, 255);">Hawking Radiation can only be applied in black holes. It occurs in a black hole until the black hole evaporates. It is simply just the black hole emitting radiation at the cost of mass. A singularity is a place where there is //no volume at all(0 volume), and where the density is infinite.// What's Hawking Radiation??? ~ LBQ (part of quantum mechanics. theorem was proved true. come up by Stephan Hawking :P Jeremy Do you even know what you are talking about??? -Daniel (P.S. I write things that i know are true.) Jeremy >:( Note to XLR8: Try right clicking the space below the sentence "If you want the answer, press Ctrl and A at the same time, or select all from the right-click control panel." ~Alex P.S. Double right click.

Question 12 Can anyone prove that i=every no.? If you can, you will be famous enough to be remember even when humans travel to a distant cosmos.

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution It's impossible because i=the square root of -1 which is impossible. That is why i can mean IMPOSSIBLE or IMAGINARY!~Alex (this is indirect resoning) i=sqr of -1... -1 sq = 1 ... 1 to the root of 4 = 1.... but i sq = -1 and -1 sq =1... so i to the power of 4 =1... means i is also 4th root of 1... so, i=1!!!!!!!!!!!!!!!!1... but then pythogoras's therom is shattered, isin't it, gerry? ~kx... P.S i hope i did not just shatter the fabric of maths... But if you said that i=1, then you are saying that, i, the square root of -1=1 which is definitly __NOT!__ So i is __NOT__ 1! Because 1x1=1. So how can the square of -1 be 1???-Daniel That is suppose to be the problem!!!!!!! =( - Gerry Let n= the number. n-(i squared+1)~ Garett if i is the 4th root of 1 then i=1=-1(because -1^4 is 1) And then -1=1 which is totally WRONG!1!!!!!!!!!~Alex p.s Gerry 121522519 51391225. Alex!!! I can read that you 20151520 PROOF THAT MY ANSWER IS CORRECT: i^1=i(obvious) i^2=-1 i^3=-i i^4=1 and -1^4=1 AND 1^4=1 Means the 4th root of 1 is 1,-1 and i. But if i=1, indirectly YOU are also saying that -1=1. Sorry, but CASE CLOSED! i CANNOT EQUAL 1! YOU 2015152019!!!!!! The last 12 lines and this line has been typed out by ALEX LIEW OF P5 RESILIENT To Alex, -1^4= -1. If you don't believe me then check with your calculator (unless the calculators are revolting). And why is i^2 and i^4 1?????? That means you are saying that ixi=1 which is totally weird and wrong-Daniel To GERRY ZHANG ZHEN RUI WHO DOES NOT KNOW A SINGLE THING ABOUT I: -1^4 indeed is -1, but THAT is because the calculators take it as -(1^4). The same thing applies when you punch in -1! on your calculator. (NOTE TO EVERYONE IN P5 RESILIENT AND P5 VICTORIOUS: -1! has NO answer. Why you get an answer of -1 is because the calculator treats it as -(1!). You will find out soon enough when you try -2!,-3!,-4! and so on. If you can't, sorry you are chicken-brained).~Alex Oh and one more thing i forgot to say: -1^4 is -1x-1x-1x-1=1(because if there is an even number of negatives in an equation the answer will be positive.). This is especially to GERRY ZHANG who does not revise his maths notes and hence should not be in AMEC. Full-stop. CASE CLOSED!!!!!=)~Alex And another thing: the 5th root of i is i(read GARETT TOK ERN LIANG'S ANSWER FOR Q7. HE GOT IT RIGHT). So ixixixixi=i^5=i Therefore i^4=1. But the 4th root of 1 is nothing special; it merely have three different answers. But if you say i=1, i must also equal -1 so you are saying that -1=1 which is wrong! Gerry has broken the basics of math. He should go back to Primary 1!~Alex Daniel, are you sure your spectacles aren't broken? I clearly put there i^2=-1. i to the power of 2 is negative 1!!!!!!!~Alex Ok, maybe I was wrong about the i^2=1 but you clearly put that i^4=1! So I hope your glasses are too low power? -Daniel Daniel, revise your math notes. Clearly it's i^2xi^2=i^4=-1x-1=1~Alex P.S. To get this symbol ~ hold shift then press the button on the left of 1. I am NOT saying i=1!!! I was just checking!!! ~ Gerry To all calculators: here is something weird. You say that -1^2 is -1. Then the square root of -1 should be -1 because it can be put as: square root of -1^2. To do square roots which have squares in them, you just have to take away the square SO ALL calculators need programming (unless yours says that -1^2=1). And I am very sorry to Alex for putting wrong things up... ~Ultra sorry Daniel. BIG debate going on Sorry Daniel, YOU ARE THE PERSON WHO PUTS WRONG THINGS UP. WHY CALCULATORS SHOW -1^2=-1 AND -1^4=-1 IS BECAUSE THEY TAKE IT AS -(1^2) AND -(1^4). IF YOU DO NOT BELIEVE ME, GRAB YOUR CALCULATOR AND PUNCH IN -1x-1 AND -1x-1x-1x-1. NOTE TO THE CALCULATORS: DO NOT BELIEVE A SINGLE WORD DANIEL TAN SAID. THE SQUARE ROOT OF -1^2, WHEN PUT IN, SHOWS MATHS ERROR DUE TO ONE OF THE FOLLOWING TWO REASONS: 1. YOU TAKE IT AS (THE SQUARE ROOT OF -1)^2 2. YOU TAKE IT AS THE SQUARE ROOT OF -(1^2) EITHER WAY RESULTS IN MATH ERROR. CASE CLOSED THE END~ALEX LIEW

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">

hen it is wrong. Hannah When it's a negative 8 and a negative 2... ~ LBQ LBQ,-8+-6=-14!!!dUH!!!-MANUKJY Which it is not!!! ~ LBQ What LBQ means that it is -8+6=-2. Is it? Or what about 8+-6=2 -Daniel

Dainel's answer is correct! LBQ,you finally got it.

Question 10 by Garett

This statement is false.

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution

This is a paradox. Suppose it is false, it would then be true and vice versa. Therefore to be false it has to be true and vice versa. To make it easier, think that the sentence is negative. True is positive and false is negative. If you say it is positive, then the sentence would still remain negative because negative+positive=negative If you say it is negative, then the sentence would be positive because negative+negative=positive Understand? -Daniel

Question 9 - by __Wei Ren__ I have a fox, a chicken and a basket of corn. I need to take them across the river using a canoe. But my canoe can only fit me and another object (object means e.g fox, chicken). And if I leave the fox with the chicken, the fox will eat the chicken. If I leave the chicken with the corn, the chicken will eat the corn. How do I get all of them across the river without losing anything?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution I get the chicken across the river first. When I return, I take the fox across. Then, I take the chicken back. After that, I take the corn across and lastly, I take the chicken across.

That is so well known, everyone knows it!!! ~ LBQ I purposely chose a well-known one ~ LWR Everyone would say that~ Garett

Question 8 by Vint Seng

If it takes 10 people to dig 5 holes in 6 hours, How long does it take a person to dig half a hole?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution It is impossible to dig half a hole!!! Vint Seng What's a half-hole?! ~ LBQ ass many ass u want- can be any size lah! 6hrs~Wan Cheng
 * LOLs*Even after seeing past answers i still cant believe people fall for it!*LOLOLOLOLOLOLOLOLOLOLOLOOLOL(Infinite LOLs)LOLOL*

Question 7 __by alex__

What is the 5th root of i, if the square root of i is (1+i)divided by the square root of 2, and the cube root is i plus the square root of 3 and the whole thing is halved?

This utterly hard-looking is actually very easy if you know the powers of i

You should know what is 5th root.

i stands for imaginary number which is simply the square root of -1.

Original question from MURDEROUS MATHS.

Don't ask so chim questions. some people in the class con't understand chimology!!!

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution

5th root of i =i Garett Duhhhhhhhhhhhhh................................................................................... why??? ~ LBQ Ask alex! Duh.............~Garett Look at this~ i squared =-1 i to the power of four= -1 x -1 = 1 so 1 x i =i~ Garett Alex, do you have an answer to 'What is the fifth root of i?' ~Mrs Lim For those who are keen in getting entangled with complex numbers, you can go to this website. [] Yes i do. garett got it right.~alex

Question 6 __by alex liew__

how many steps does it take to make 691 a palindrome?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution By Jeremy Tian of P5 Resilient Go to the html below [] It explains that 691 will NEVER form a palindrome!!!

Question 5 __by kx__

Can you use 8 matchsticks to form... 2 squares and 4 triangles? You cannot split the squares into triangles and cannot overlap any either!!! Also, I have a brain teasers book and a riddles and brain teasers book.

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution Provided by kx's classmate alex

FORM 1 SQUARE WITH 4 MATCHSTICKS FIRST THEN FORM ANOTHER SQUARE WITHIN THE 1ST SQUARE AND TILT IT AT AN ANGLE OF 15 DEG., THEREBY FORMING 4 TRIANGLES AND 2 SQUARES.

Thinking it should be an angle of 45 degress ~ LBQ Are all the Matchsticks of the same length?- Garett Hello?! I said it should be 45 degrees not 15!!! ~ LBQ I said it should be 45 degrees not 15!!!!!!!!!! ~ LBQ Is anyone listening??? ~ LBQ I guess not~ Garett You cannot listen on a computer! So how would listen in the first place??? -Daniel CAN BE ANY DEGREE BUT MUST FIT.-KX Note: It can't be 0 degrees, nor can it be 90, 180 or 270 degrees in the first place to what kx said is wrong~ garett

Question 4 __By: Alex Liew__

You have 3 numbers a,b and c. When a is multiplied by b it is equal to c. Then a squared times b squared = c squared.

Why?

For example a=2 b=3 c=6 Perfect as 2x3=6 right? now 2 squared=4 3 squared=9 4x9=36 And the square root of 36 is 6.

Another Example a=10 b=20 c=200 a squared= 100 b squared= 400 100x400=40000 And again 40000 is the square of 200

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution It is proved by Pythagoras (Or was it Archimedes?) - Gerry I WANT SOLUTIONS, NOT A SENTENCE STATING WHO PROVED THE STUFF!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~The person that typed out this question! Gerry, would you like to travel back in time to ask Pythagoras or Archimedes?~Alex I guess so (even though I am not Gerry) ~Daniel

Question 3 __By: Choo Zheng Chen__ Thirteen teachers are in Paradox, New York attending a math conference. When they arrive at the Enigma Hotel to check in, they are told that only 12 rooms are available. Since their school had made reservations for 13 rooms, the teachers are a bit upset that they will have to find another place to stay. As they are preparing to leave and find another hotel, the manager comes out and asks if there is a problem. When she hears of their situation she assures them that the Enigma Hotel has enough space to accommodate each teacher in his or her own room. She takes two of the teachers to room #1 and promises to come back in a few minutes and take one of them to another room. She takes the third teacher to room #2, the fourth teacher to room #3, the fifth teacher to room #4 and so on, taking the twelfth teacher to room #11. She then returns to room #1 and escorts the extra teacher waiting there to room #12. All of the teachers are now happily settled in their own rooms. Is this possible? Why or why not?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution

If you number the teachers so that the first two is Teacher 1 and 13. Now Teacher 2 goes to Rm 2 Teacher 3 to Room 3 Teacher 4 to Room 4 Teacher 5 to Room 5 Teacher 6 to Room 6 Teacher 7 to Room 7 Teacher 8 to Room 8 Teacher 9 to Room 9 Teacher 10 to Room 10 Teacher 11 to Room 11

Now the manager takes Teacher 13 to Room 12.

Solution Provided by Alex Liew of P5 Resilient

So one question still remains though: WHO IS TEACHER 12???????????

again this is alex

i thought of this. THIS IS POSSIBLE DUE TO THE FOLLOWING REASON

NO ONE EVER SAID THAT THE 12 ROOMS MUST ACCOMODATE 1 PERSON each.

Are you sure that that is the solution coz' in his brain teaser, at the very end he said :"Why or Why not?"- Garett

There's always an extra room for women- The ladies's room/ the toilet Garett the 12th teacher coul'd be the manager herself.-kx

HAHAHA! THINKING ABOUT THIS TICKLES ME! TWO OF THE TEACHERS ARE SIAMESE TWINS(which means two parts of their body parts are joined!) LOLOLOLO,OOLOOLOL-Alex

teacher 1 to 12 goes to room 1 to 12. teacher 13 sleeps in room 1's cupboard --Jeremy

ermm, Zheng Chen said that each teacher have their own room... - [|FWcheng]

Solution from Wei Ren Teacher 1 and 2 in Room 1 Teacher 3 in Room 2 ...... Teacher 12 in Room 11 Teacher 13 in Room 12 Teacher 1 has nowhere to go to now so... THIS QUESTION IS IMPOSSIBLE!!!

It's impossible cause the teacher 13 suddenly disappeared into thin air!~Wan Cheng No offense to MR Choo, but... HOW IS THIS RELATED TO MATHS AT ALL? BTW, have a look at this. 13 Teachers, 12 Rooms possible solution.ppt** (And no flaming whatsoever for slide 9)

Question 2 __By: Lee Bing Qian__ 5, 17, 43, 89, ___,__ _

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution

5 = 1^3 + 2^2 17 = 2^3 + 3^2 43 = 3^3 + 4^2 89 = 4^3 + 5^2

And so the formula is n^3+(n+1)^2

5^3 + 4^2 = 125 + 16 = 141 6^3 + 5^2 = 216 + 25 = 241

Question 1 __By: Lee Bing Qian__

Which two numbers when multiplied together gives you 100000 if none of the numbers end in zero?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution As 10000 is equal to 105 it also equals to 25 x 55 2^5 = 32 5^5 = 3125 So 32 x 3125 = 100000