ASF Puzzles & Conundrums Thread

[bellenuit]

An easy one for those still up this late......

You have 4 pieces of paper. On one side of each piece of paper is a number, on the other a letter. The pieces of paper are laid out in front of you and the sides facing up shows these 4 letters/numbers: E K 4 9

What is the minimum number of these and which ones must you turn to prove the following rule is true: "if a piece of paper has a vowel on one side, the other side must have an even number".

Which must you turn and why?

Answers in the spoilers thread please.

 

[bellenuit]

A harder one........

You have a 99 X 99 squared draught board and an unlimited supply of draughts. The colour of the squares or of the draughts are not important for this game. Initially the board is clear of draughts. You play the following game against a single opponent. Each player must in turn place a draught on the board, but it can only be in an empty square that doesn't have a draught in any of the 8 squares surrounding it (e.g. doesn't have a draught in any of the immediately adjacent squares either horizontal, vertical or diagonal to the square you want to place your draught in). The first player that is unable to place a draught loses.

You get to go first. What game strategy should you use to ensure you always win.

Answers in the spoilers thread please.

 

[trainspotter]

TAKE a look at the two wheels in the image above. Which one is moving faster?

 

[bellenuit]

Another in the same vein as the Blue Eyed Slaves.

Prison Numbers

Two of the kingdom's finest logicians are caught embezzling the kingdom's coffers and are sentenced to life imprisonment in separate solitary confinement. The king, a puzzle addict, decided to give them a chance of freedom, and posed the following challenge to them.

Each was separately asked to think of an integer greater than or equal to zero and tell it to the jailer who reported both numbers to the king. The king then had a messenger convey this message to both prisoners:

"Each day at 5pm, the jailer will come to your separate cells and give you the opportunity to tell him what number the other prisoner thought of and if you are correct, you will be freed. You can only arrive at the answer through logical deduction and guessing or cheating in any way is out of the question (there are horrible consequences for doing so). If you have logically deduced the number the other prisoner thought of you must tell the jailer, otherwise you just say you do not know. In the latter case the jailer will tell you, after he has heard the other prisoner's response, whether the other prisoner is to be freed or not that day."

With both thinking this is an impossible challenge, the messenger then added: "To assist you, the king has said that the sum of both numbers is either 10 or 13."

On the 5th day, both prisoners are freed. What were the two numbers that they thought of? How did you arrive at this conclusion?

Answers in Spoilers thread please.

 

[bellenuit]

A hardish one for the weekend.

Box of Marbles of Four Colours

A father comes home and gives his maths prodigy daughter Mary a box of marbles as a present. "This box contains marbles of 4 different colours; red, green, blue and yellow. There are more red than green, more green than blue and more blue than yellow" said the father. "How many of each colour are there?" asks Mary. "You tell me" says the father and adds "I can tell you that in total there are fewer than 18 marbles and that the product of the four numbers is the same as our house number" Mary thinks for a while and then says "I need to know a bit more. Is there more than one yellow marble?" As soon as the father replies, Mary says "I've worked it out" and correctly states the number of each colour.

Knowing her own house number and whether or not there was more than one yellow marble, Mary found the problem trivial.

Based on the above information only, you can now work out the number of marbles of each colour. How many of each are there and give your bullet proof reasoning for you to arrive at those numbers?

Answers in the Spoilers thread please.

 

[SirRumpole]

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.



May 15, May 16, May 19



June 17, June 18



July 14, July 16



August 14, August 15, August 17



Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.



Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.



Albert: Then I also know when Cheryl’s birthday is.



So when is Cheryl’s birthday?

 

[bellenuit]

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.

SirR, this has been posed already. See #5 on this thread.

 

[SirRumpole]

SirR, this has been posed already. See #5 on this thread.

My apologies

 

[cynic]

My apologies

I got really excited when I logged in to and saw an update to this thread thinking "Oh goody! Another delightful puzzle!!".

As soon as I realised it was a repeat, my excitement was quickly replaced by disappointment.

However, I am sincerely appreciative that yourself and others have willing put in the time and effort to offer ASF some terrific puzzles.

 

[SirRumpole]

I got really excited when I logged in to and saw an update to this thread thinking "Oh goody! Another delightful puzzle!!".

As soon as I realised it was a repeat, my excitement was quickly replaced by disappointment.

However, I am sincerely appreciative that yourself and others have willing put in the time and effort to offer ASF some terrific puzzles.

You're welcome Cynic,

Maybe the last word on the ABC puzzle

 

[bellenuit]

This (old) one appeared on a newspaper blog today, so some of you may have seen it. For those who haven't, here goes:

Increasing the Ratio of Women in the Population.

A king (dirty old leech) decided that there should be proportionally more women in his kingdom than the current 50%. He knows that the probability of a girl at birth is exactly 50% and that males and females have on average exactly the same lifespan (in his kingdom anyway), so he assumes this strategy will work.

He orders that couples should strive to have as many children as possible, but only under the following conditions:

1. If they have a female baby, they are to have no more children.
2. If they have a male baby, they are to continue to have children until condition 1 is satisfied.

Question 1: Will that strategy increase, reduce or make no difference to the proportion of women in the population.

Question 2: With only recourse to edicts of the above kind (when to reproduce and not reproduce etc.) and without recourse to unsavoury methods such as infanticide, forced emigration or things similar, what, if any, would be the optimum policy to adopt to achieve an increased proportion of women in the population. (I know this part is going to cause a lot of controversy).

Answers in the spoilers thread please and the reasoning for your conclusions are required.

 

[bellenuit]

An easy one that can be solved with no math, just some logic.

A plane flies in a straight line from Perth to Sydney, then back in a straight line from Sydney to Perth. It travels with a constant engine speed (constant air speed) and there is no wind. Will its travel time for the same round trip be greater, less, or the same if, throughout both flights, at the same engine speed, a constant wind blows from Perth to Sydney?

Answers in Spoiler thread please.

 

[bellenuit]

This one is not so easy......

Four people with different physical ailments are at the edge of a wide raging river that they must cross to escape from a bushfire quickly heading towards them. The river is spanned by a rickety old rope supported timber batten bridge that can only hold two people at a time.

Because of their physical ailments, the four cannot cross the bridge at the same rate. A can do it in 1 minute, B in 2, C in 5 and D in 10 minutes.

It is nighttime and they have just one dim flashlight between them. Without the flashlight, trying to cross the dilapidated bridge would mean certain death. Since two crossing must share the flashlight, they can only cross at the pace the slowest of the two is capable of.

What is the quickest time all four can get safely across the river and how?

Answers in Spoilers thread please.

 

[bellenuit]

You have the four 3-link chains shown on the left. Your task is to join them together to form the 12-link chain on the right. Each link has a single cut through it that can be prised open to join (or unjoin) two links and then is prised closed.

What is the minimum number of links that must be prised open to allow the 12-link circle to be formed. Explain method used.

Answers in Spoilers thread please

 

[bellenuit]

Five similar puzzles that I came across today in increasing complexity. You are to find the missing value in each of the following images (answers in Spoilers Thread).......

Note: For all puzzles, all answers are whole numbers (no fractions). The instructions are a bit ambiguous, but I also understand that to solve the puzzles you do not need to deal with fractions.

Number 1

 

[bellenuit]

Number 2

 

[bellenuit]

Number 3

Note: I can confirm that having now solved Number 3, that 1, 2 and 3 can be solved without resorting to using fractions in interim results. I assume the same applies to 4 and 5.

 

[bellenuit]

Number 4

 

[bellenuit]

Number 5

 

[bellenuit]

A fairly easy one.



You have a board marked into a grid of 20 X 20 squares. You also have rectangular dominoes that are two grid squares in size, like the one shown above. Clearly you could cover the total board surface with 200 of these dominoes if they are laid flat, each covering two squares ((20 * 20) /2).

However, two diagonally opposite corner squares are cut from the board as shown above. Is it possible to place 199 dominoes flat down on the board so that they completely cover the remaining surface of the board?

If yes, prove it. If no, prove it.

Answers in Spoilers thread.