Archive+Puzzles+21+to+40

Question 40-Alex

Kenneth and Karla had 256 marbles each. Kenneth gave half of his marbles to Karla. Karla then gave half of her marbles to Kenneth. In total, they did this process thrice. How many marbles did Karla have in the end?

Solution 40

Hint: When i got to the part about Karla giving her marbles, it means the new amount(which is her original+what Kenneth gave).

After 1st time

Kenneth: Karla 310 202

1st and half time....

155 357

It is odd no.s ........~Garett

Karla-->Kenneth 128 marbles Kenneth:Karla 128:384 Kenneth-->Karla 192+128=320. u r wrong unfortunately cause after first round Kenneth would have 320 marbles, not 310.(192+128=320, not 310)~Alex

Kenneth : Karla 1st time: 128 : 384  2nd time: 320 : 192 3rd time: 160 : 352 4th time: 336 : 176 5th time: 168 : 344 6th time: 340 : 172 Karla had 172 marbles in the end.~Yi Rui Correct~Alex

Question 39- Alton

A man wanted to get into a members only club so he hid and watched the guard at the door of the club house. The guard said a number to each member as they approached, and the member would respond with a number of their own. If the member responded with the correct number they were let in. If they responded incorrectly they were thrown out. One member came up to the door, the guard said twelve, and the member responded with six and was let in. Another member came to the door, the guard said six and the member responded with three and was let in. Believing he had heard enough, the reject went up to the guard. The guard said ten, and the reject said five, but was not let in. What should the reject have said?

Solution 39

If anyone does not solve this by Friday, I'll give out the answer. There was no member with number 5.lolz~Alex The reject should have said: I'm a trespasser, pls arrest me, number 1. Guard: One? Good!(Kicks the reject in)~Alex  Eight~Garett All of you are wrong... Try again.... ~ Alton Probably involves factors... Eighteen.~Alex Still wrong! XD ~ Alton Two~Garett Four~Alex bash up the guard Everyone is STILL WRONG! XD ~ Alton 3 or 0? ~ WeiC Since its Friday, I'll give out the answer. 3! Reason: The number of letters in what the guard said. ~ Alton So I'm half correct in my solution! ~ WeiC LOL. Two(Garett's ans)---Three(correct answer)---Four(my answer). OMG.~Alex Alton, there is more than one correct answer. Garett's first answer, eight, was probably because 12 and 6 - let in, 6 and 3 - let in, 10 and 5 - not let in... 1 + 2 +6 = 9 and 6 + 3 = 9 and so... 1 + 0 + ? = 9...1 + 0 + 8 = 9.. so...there is more than one correct answer. ~ FWC Wei Cheng, I don't get what you mean. Can you explain it in another way? ~ Alton I just meant that there IS more than one way to this question. - [|FWcheng] Wei Cheng, what I mean is, I don't know how you got the other answer. Explain it again. -_- ~ Alton 12 x 6=72 6x3=18 72/18=? 18x3=54 54+18=72 72/18=4 Since it is 4... 10x?=4 Correct Ans:2/5~Alex

Well Alton, check this out: Guard's no Member's no. 12 6 : 1+2+6=9 6 3 : 6+3=9 10 ? : 1+0+?=9

so, ?= 8 ~garett (thx wei cheng) hmmm... Ok... I get it. I can accept his answer then. (P.S. I didn't think of that!) ~ Alton

question 38- Alton

Imagine you are in a sinking rowboat surrounded by sharks. How would you survive?

Solution 38

If anyone does not solve this by Friday, I'll give out the answer.

Have Shark fin's soup!~Jun Yuan Stop imagining it....~Garett Use a chopper to rescue yourself(chopper as in the helicopter)~Alex Jun Yuan's answer: WRONG! Garett's answer: CORRECT! Alex's answer: WRONG! Ohhhhh 198920...~Alex How in the world is this related to Maths? This is related to maths, as you need to use your brain XD. e.g. Q37 ~ Alton Just relax(dun struggle), or poke their noses to drive them away. Or just await your death peacefully and then be reincarnated. Wait, is there a hole in the rowboat or is it just that it is heavy? If it is heavy, turn it upside down, stand on the upper side of the boat and row. Vint Seng. Then all your belongings will fall into the sea, and when you get to land you commit suicide becuz your teddy bear fell into the sea~AlexDo the SharkBoy and LavaGirl thingy.~Jun Yuan

Question 37-Alex

Sheryl, Sharon, Shawn, Shah and Shola were playing in the backyard when one of them broke the vase. This was what they said:

Sheryl: Either Sharon or Shah broke it. Sharon: I am innocent. Shawn: Shah didnt do it. Shah: Shola didnt do it. Shola: I am not guilty. I think Shawn, or maybe Shah broke it.

Who broke the vase assuming only one lied?

Solution 37

If Sheryl was lying, then it will contradict Shawn's statement. So, it is true! If Sharon was lying, then she will contradict Sheryl's statement. True again! If Shawn was lying, Shah did it. But, this doesn't contradict any statements. So, false!

Double check: If Shah was lying, Shola did it. This contradicts Shola's statement. True! If Shola was lying, Shola did it. But then it contradicts Sheryl's and Shah's statement. True once more!

Shah was the one who broke the vase. ~ Alton Thumbs up to the solver~Alex Welcome then. ~ Alton You copied my question!! Cheater!! DEFAME DEFAME!!!!!!!!!!!!! ~Vint Seng AND WHY? What is ur question???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????~ALEX

Question 36- Alton

First calculate 100 + 50. Next, divide your answer by five. Finally, add 4 to your number. What would the number be?

Solution 36

(100+50)/5+4=34~Alex

lolz

Wrong! Try again! ~ Alton

If no one solves this by Friday, I will give out the answer. ~ Alton Your number + 4~Alex Since its Friday, I'll give out the answer. 304, 340, or 430! Reason: Add four to your number. The number is 30, so add the number anywhere to the number. ~ Alton

Question 35-Alex

1 is a prime number. True or False?

Solution 35

False! ~ Alton Proof? ~Alex An integer //greater than one // is called a prime number if its only positive divisors (factors) are one and itself. ~ Alton It is not true and not false. Because the definition of a prime number is that it can be divide by two numbers, 1 and itself. If we look at 1, it can be divided by 1 and itself (which is still 1). But a prime number has to be able to be divided by two numbers. 1 and 1 is the same number. ~Gerry Gerry has the best answer.~Alex

Question 34- Alex

Karl, Kevin, Kim and Kieran went fishing. There were 2 types of fish in the water: mackerel and sardines. This was what they said afterwards:

Karl: The total number of my fish is 8. Kevin: The difference of the two different catches is 4. Kim: The product of my 2 catches are 16. Kieran: I'm not good at counting. I only remember that I caught 2 less sardines than Karl, but 1 more mackerel than Kevin.

If each person caught 8 fish, how many mackerel were caught in total?

Solution 34

Karl: 5 mackerel 3 sardines Kevin: 6 mackerel and 2 sardines Kim: 4 each Kierean: 7 mackerel 1 sardine

22 mackerel were caught altogether.~Garett

Question 33- Alton

A vacationing family sitting around the campfire has the following conversation:

1. Father: What day is it? I am sure it isn't Tuesday, Wednesday or Thursday. 2. Mother: Well, that's not very helpful dear. Besides, yesterday was Friday. 3. Father: No, now that I think about it, yesterday wasn't Friday, tomorrow is Friday. 4. Jon: The day after tomorrow is Thursday. 5. Meg: You are wrong. Tomorrow is Thursday. 6. Mother: Actually, it's probably Thursday today. 7. Jon: All we know for sure is that it wasn't Sunday yesterday.

If only one statement above is true, what day of the week is it?

<span style="font-size: 16pt; color: rgb(51, 102, 255);">Solution 33 If statement 1 is true, today cant be Tuesday, Wednesday, Thursday, yesterday is sunday(Statement 7), but contradict statement 3(which will mean yesterday is friday, tomorrow isnt friday. Statement 1-False. If statement 2 is true, today is Saturday. Yesterday was friday, tomorrow isnt. But statement 7 states that if it was false yesterday was Sunday. Statement 2-BOGUS! If statement 3 is true, Today is Thursday,which agrees with statement 1. Yesterday wasnt friday. But statement 6 would be true. So, wrong! If statement 4 is true, Today is tuesday. But statement 3 says yesterday was friday. If statement 5 is true, today is wednesday.See statement 4. If statement 6 is true, Today is thursday. see statement 3. If statement 7 is true, it is either tuesday, wednesday or thursday. yesterday wasnt friday. ARGHHHHHHHHHHHHHHHHHHHHHHHHHHHHH!

wth~Alex

So, what is your answer? ~ Alton Statement 8: It's either Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday tomorrow.~Alex

What day is it then??? If anyone doesn't answer this by Friday, I'll give out the answer. ~ Alton This question is totally OMFG because statement 2 and 3 contradict each other. My final answer: Saturday. THIS IS INSANE! DEFAME!~Alex

Statement 2: Saturday as Statement 7 says FOR SURE......~Garett

Both of you are wrong! Try again! XD ~ Alton Monday- S1True, S2False, S3False, S4False, S5False,S6False,S7False. Answer: Monday~Alex Finally, someone got it correct. ~ Alton

<span style="font-size: 16pt; color: rgb(255, 0, 0);">

Question 32- Alton

A bridge, 2 miles long, is rated for 12,000 lbs. Even one ounce more will cause it to collapse. A truck weighing precisely 12,000 lbs begins to cross. At the halfway point, a sparrow weighing 5 ounces lands on the truck. The bridge does not collapse. Why?

<span style="font-size: 16pt; color: rgb(51, 102, 255);">Solution 32

Halfway through the truck would have lost at least 5 ounces of fuel. There would be no accident as it still weighs precisely 12,000 lbs.~Alex Correct! ~ Alton I've seen this question before... long before you uploaded it.~Alex

<span style="font-size: 16pt; color: rgb(255, 0, 0);">Question 31- Alex

In the MAS, the money machines suddenly go on strike becuz they are not being recharged properly and end up burning the whole mint. Insufficient materials could not make more machines, and Singapore's economy fell into a slump. One day, Professor M Money went to the MAS and told them he has three special money machines that could make money. They work totally on solar power, and they do not go at the rate the MAS machines go. A regular MAS money machine goes at 40 $2/hour. Machine 1 goes at 35 $2/2 hours, Machine 2 goes at 70 $2/1 minute, and Machine 3 goes at 36 $2/day. Because these machines work on solar power which means they can only operate for 11 hours every day, unlike MAS machines which can run 24/7. Question: If the 3 machines were compared to 9 MAS machines, whose machines earn more money in 6 weeks? The seemingly generous Professor Money's, or the seemingly lazy MAS'? (No offense to everything in here...)

<span style="font-size: 16pt; color: rgb(51, 102, 255);">Solution 31

lolz. if noe one solve this i will. MAS machines-40 $2/hour. 24 hours-1 Mas machine produces 960 $2 a day. 960x9x42=362880 notes. Machine 1- 35 $2/2 hour. 11 hours- 35x5.5=192.5 round to 192 notes/day. Machine 2- 70x60x11=46200 notes a day. Machine 3- 36 $2 notes a day. 192+46200+36=46428 notes. 46428 notes x 42 days= 1949976 notes!!!!!!!!!!

1949976>362880!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Cant believe why no one can solve my question~Alex

<span style="font-size: 16pt; color: rgb(255, 0, 0);">Question 30- Alex

3 chicks and 3 wolves want to cross the river. Their sole instrument of crossing the river is a raft that can only hold 2 animals at a time. However, if there are lesser chicks than wolves at any side of the river, the chick(s) will die. For example, if there are 2 chicks and 3 wolves at 1 side of the river, the 2 chicks will die. If there are 2 chicks and 2 wolves at 1 side of the river, the chicks will not die. If there are 2 chicks and 1 wolf at 1 side of the river, the chicks will not die, though the one on the other side will die. The question is: How to get all 6 animals across the river without anyone dying? Remember: WITHOUT ANYONE ON THE RAFT, THE RAFT WILL NOT MOVE AUTOMATICALLY ACROSS THE RIVER!

<span style="font-size: 16pt; color: rgb(51, 102, 255);">Solution 30 First move 1 chick and 1 wolf across. Then take 1 wolf back to the other side. Now, take the 2 remaining chicks to join the other chick. Take 1 chick back, and bring 2 wolves there. Take one wolf back, and take one chick and one wolf there. Take 1 chick back and bring the last wolf with the chick there. All the animals are now across the river. ~ Justin WRONG! Because there cannot be 3 wolves and 2 chicks on one side of the river! Side A Side B 2 C, 2 W 1C,1W 2 C, 3W 1C Pls read question carefully!~Alex P.S. You need at least 10 moves to solve this. Side A Side B 3C, 3W 0C, 0W 1)Move 2 wolves across 3C, 1W 0C,2W 2)take a wolf back 3C, 2W 0C, 1W 3)Move two wolves across 3C, 0W 0C, 3W 4) take a wolf back 3C, 1W 0C, 2W 5) move two chicks across 1C, 1W 2C, 2W 6) take a chick and a wolf back 2C, 2W 1C, 1W 7)bring two chicks across 0C,2W 3C, 1W 8)take a wolf back 0C, 3W 3C, 0W 9) Bring two wolves across 0C,1W 3C, 2W 10)take a chick back 1C,1W 2C, 2W 11) take the last chick and wolf across 0C,0W 3C, 3W ~Garett

Wei Ren 1) one chick one wolf across river (2C2W, 1C1W) 2) bring one chick back (3C2W, 0C1W) 3) bring two wolfs across (3C0W, 0C3W) 4) bring one wolf back (3C1W, 0C2W) 4) bring two chicks across (1C1W, 2C2W) 6) bring 1 wolf back (1C2W, 2C1W) --> anyway i am still with chicks so wolf cannot eat chicks 7) bring one chick and one wolf across (0C1W, 3C2W) 8) bring one wolf back (0C2W, 3C1W) 9) bring two wolfs across (0C0W, 3C3W) If the part at no. 6 is wrong (but i think there is logic in it), then Garett's answer should be the best.

First Try by Justin- WRONG!(At move 2) Second Try by Garett- CORRECT! Third Try by Wei Ren- BOO!(Move 6)

As long as you have more wolves than chicks on 1 side then you lose. And as i told you, you cant solve this in 10 moves or less. if you cant, dont act smart!~Alex Humans do not play a role here. If they do they would have killed all 6 animals for some wolf stew and chicken wings. And I said that " can only hold 2 animals at a time." Did i mention humans? No!

Question 29 - Mrs Lim Some time back while in England I came across a case in a criminal court. A man was being accused of having stolen certain valuable jewels and trying to run away with them, when he was caught by a smart police officer who overtook him. In cross examination the lawyer for accused asked the police officer how he could catch up with the accused who was already twenty seven steps ahead of him, when he started to run after him. 'Yes sir,' the officer replied. 'He takes eight steps to every five of mine.' 'But then officer', interrogated the lawyer, 'how did you ever catch him, if that was the case?' 'That's easily explained sir,' replied the officer,'I have got a longer stride...two steps of mine are equal to his five. So the number of steps I required were fewer than his, and this brought me to the spot where I captured him.' A member of the jury, who was particularly good at quick calculations did some checking and figured out the number of steps the police officer must have taken. Can you find out how many steps the officer needed to catch up with the thief?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution 29:

30 steps 5(30/2) = 75 8(30/5)+27=75 And the accused is caught!!!!!! ~Garett

Question 28 - Vint Seng

Four friends, Edwin, Fred, Gary and Howard, were playing together when one of them acidentally broke a vase. The teacher asked: "Who is the culprit?" Both Edwin and Howard said: "Not me. I did not break the vase." Fred said: "Howard broke the vase. It wasn't me." Gary said: "I say that Fred is the culprit." (a) If only one of them was lying, _ broke the vase. (b) If two of them were lying, _ broke the vase. <span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';"> Solution 28: a) Fred b)Horward ~Garett

If Edwin lied, Fred's statement would contradict Howard's and Gary's statement contradicted Fred's. If Howard lied, Gary would say the opposite of what Fred said. If Gary lied, Fred would contradict Howard. If Fred lied, Edwin told the truth, Gary did and howard did!

Question 27 - Mrs Lim

There are 150 members in a Ping Pong CLub. We decided to have a tournament. All members came forward to play in the game. Every time a member loses a game, he is out of the tournament. There are no ties. Can you tell how many games must be played in order to determine the champion?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution 27: 149 games must be played ~Daniel 75 games played:Result:75 advance,75 kicked out. 1 person is singled out for later. 75-1=74. 37 games played: 37 advance, 37 out. The extra person is put in the next round:37+1=38 19 games played:19 advance,19 out. 1 is taken out for later. 9 games played:9 advance,9 out. The extra man is put inside. 5 games played: 5 advance, 5 out. Another one taken out for later. 2 games played: 2 advance 2 out 1 game played: 1 advance 1 out. Just dump the extra guy versus this winner. 1 game played: CHAMPION REVEALED! 75+37+19+9+5+2+1+1=149. 149 games played~Alex

That's correct! Another way to solve this problem is to see that after each match, one player is eliminated. To eliminiate 149 players, 149 matches have to be played. ~Mrs Lim

Question 26 - Mrs Lim

Using each of the digits 1 to 9 exactly once only, replace each question mark by a digit such that ??? + ??? = ???

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution 26: (multiple solutions exists)

291+384=675~Alex

Has anyone found other solutions? ~ Mrs Lim

138 + 429 = 567 also works! ~ WeiC 127 + 359 = 486 also works! ~ WeiC 186 + 273 = 459 also works! ~ WeiC 286 + 173 = 459 also works! ~ WeiC 438 + 129 = 567 also works! ~ WeiC 391 + 284 = 675 also works! ~ WeiC 327 + 159 = 486 also works! ~ WeiC 276 + 183 = 459 also works! ~ WeiC 176 + 283 = 459 also works! ~ WeiC

Question 25 - Mrs Lim Mr Lau wanted to encourage his son to study math. For every problem correctly solved, he would give his son 15 cents. For every incorrect solution, his son must give him 10 cents. At the end of 50 problems, neither owed any money to the other. How many problems did the son solve correctly?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution 25: LCM(10,15)=30 10x3=30 15x2=30 For every 5 questions, Mr Lau's son answered 2 correctly and 3 wrongly. 50/5=10 2x10=20 Mr Lau's son solved 20 questions correctly.~Alex

You've got it correct again, Alex. Good job! ~ Mrs Lim

Question 24 - Mrs Lim

Using your mental calculator, can you compute accurately the sum: 1.9 + 1.99 + 1.999 + 1.9999 + ... + 1.999999999 ?

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution 24:

17.888888889~ garett Congrats for being the first to answer this question correctly. Did you add mentally or used 2 x 9 - 0.111111111 ? ~Mrs Lim I added up to +1.999 when I figured this pattern out: (let n be the number of nines in x) the sum of all the numbers until x equals to 2n-1. (note: the dot after 2n-1 is not a full-stop. It is a decimal point.) n-1 number of 8s before ending with 9 so...~ garett Looking for a pattern is one way of solving math problems. Good attempt! ~Mrs Lim

Question 23 - Mrs Lim

See this video on matchstick puzzle. Click pause immediately after the question so that you can try to solve the problem before the answer is revealed.

Move the horizontal matchstick towards the left or the right. Stop when the tip of the matchstick reaches the bottom matchstick. Now move one of the vertical matchsticks on the top.It depends on the direction you move the horizontal matchstick(if the horizontal matchstick go towards the left, you take the right matchstick. If it goes right, take the left matchstick). Move the vertical matchstick to the tip of the horizontal matchstick that is NOT touching the bottom matchstick... and IT'S DONE!~Alex

Question 22 - Mrs Lim

See this video on matchstick puzzle. Click pause immediately after the question so that you can try to solve the problem before the answer is revealed.

Question 21 - Mrs Lim Given that a, b and c are different whole numbers from 1 to 9, find the largest possible value of (a+b+c)/(a x b x c). (2007 Math Olympiad)

<span style="font-size: 16pt; color: rgb(51, 102, 255); font-family: 'Budmo Jiggler';">Solution 21:

About the abc:

is it a x b x c or abc

for example is it 1 x 2 x 3 or 123?~Alex It should be the product of a, b and c. Thank-you for clarifying. ~ Mrs Lim 4? ~ LBQ LBQ, what are your values of a, b and c? You may have to think through the problem again. ~ Mrs Lim 1? Even though i feel that there is something weird about it a=1 b=1 and c=3~ Garett Sorry, read the question carefully: a, b and c are different whole numbers. ~ Mrs Lim I'm sorry about the typo. b was meant to be 2. I wrote too fast~ Garett Ok, this will make your solution (1+2+3)/(1x2x3) = 1. What happens when you choose other values of a, b and c? ~ Mrs Lim As when larger numbers multiply each other, the product would then be bigger then its sum, and so I had to choose the smallest three numbers. If the numbers could be repeated, I would choose three ones as if I chose 1 only, there would then be a sum of 3 and a product of 1. ~ Garett Bingo! Good observation of what happens to the product and sum when you use other bigger numbers. ~ Mrs Lim