Puzzlers

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Joe

1: You have a 4 oz glass and a 9 oz glass. Using just these two glass, and unlimited supply of water from the tap, can you accurately measure every amount of water (in whole ounces) from 1 oz to 9 oz?

 

2. Three prisoners are stood in a row, all facing forward, so that the prisoner at the back can see the front two, the middle prisoner can see the guy in front, and the front guy can see no one. The warden has 3 black hats and 2 white hats. He puts a hat on each of them.

“I don’t know what colour my hat is,” says the guy at the back

“Then I, also, don’t know what colour my hat is,” says the middle guy.

“Then I know what colour my hat is!” says the front guy.

What colour is his hat?

 

3. Adam, Belinda and Charlize go out for dinner. They each order the $10 special. At the end of the meal they each chip in $10. The waiter takes the $30 to the owner, who says “Adam comes here all the time, I’m going to give him a discount.”

The owner gives the waiter $5 in coins to give back to Adam, but the waiter thinks to himself “Adam is a cheap bastard, he never tips.” Secretly, the waiter pockets $2, and gives the remaining $3 back to Adam, who shares it with his friends.

They each go home with $1 in their pockets, having paid $9 each. 3 x $9 = $27, plus $2 that the waiter keeps is $29. Who has the missing dollar?

 

4. Someone has ten bags of diamonds. There are 10 one-carat diamonds in each bag.  All of the diamonds are identical, except that one bag is filled with fake diamonds, which are indistinguishable from real diamonds except that they are a tiny bit (say one grain) lighter. Luckily, they have a really accurate digital scale. Unluckily, the scale batteries are almost flat – there is just enough left to turn it on once, get a single numerical reading, then it will be flat. How, using just this reading, can the person determine which bag contains the fake diamonds?

They can take the diamonds out of the bags, put them in different bags, weigh all of the bags or some of the bags, put some of the diamonds in one bag and mix them all up… whatever they want. But once they’re ready, and they’ve placed the diamonds on the scale however they like, they can turn the scale on and take one single reading…

 

5. You catch up with a friend of yours that you haven’t seen since childhood. You know they have two children of their own, but you don’t know the age or sex of either child. As you arrive, you see a boy playing in the yard – is their other child more likely to be a boy or a girl, or is it the same probability?  Does it change the probability if you know that the one you saw playing is the older child?

For this question, you can asssume that there is always a 50/50 chance of having either a boy or a girl, and that having a child of one sex does not in any way alter the chances of giving birth to a second child of the same sex, ie., it’s 50/50 for the second child as well.

 

6. A warden offers all of his prisoners the chance to play a game and maybe escape. If they choose to play, then on the next day they will be led out into the yard and stood in a row, each man facing the back of the man in front, such that the last prisoner can see all of the other prisoners but the first prisoner can see no-one. Then the warden will put either a black or a white hat on each man. The proportion and distribution of black and white hats will be random – if, say, there were 813 prisoners, there might be 376 black hats, or just 13 black hats, or all black hats… no one knows. Starting with the guy at the back, each prisoner takes it in turn to say either ‘Black’ or ‘White’. Once they are all finished, if the colour they said matched the colour of hat they are wearing, they will be immediately released. If it didn’t… they will be immediately executed.

The prisoners discuss this amongst themselves, then realise that (with the exception of one person) there is a way that they can guarantee that all of them will be able to say the colour of their hat, and be released. They draw straws to be the unlucky guy… who still has a 50% chance of getting out!

What is their strategy, and who is the unlucky guy?

 

7.

 

8. There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow.

Hannah eats a random sweet from the bag. She then eats another random sweet from the bag.

The probability that Hannah eats two orange sweets is 1/3

Show that n^2 – n – 90 = 0

 

9. You are through to the last round of a game show. The host shows you three doors – behind one is a car, behind the other two are goats

you choose your door, and go to stand by it, but before you open it, the game show host tells you to stop. He opens one of the other two doors, which you didn’t choose, and shows you a goat.

should you change doors?

 

10. You are standing outside of a locked room. Inside, there is a single light bulb hanging at eye level. On the outside, next to the door, there are 3 light switches. You need to work out which switch controls the light inside – the other two are duds.

You can do whatever you like with the switches, but once you put your hand on the door you can’t touch them any more. At that point, you have to open the door, go into the room, and based on the state of the light bulb, identify which is the correct switch.

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  • Joe

    11. Take 2 packs of cards and remove the jokers. Now shuffle all of the remaining (104) cards, then divide them into two even piles, pile A and pile B, with 52 cards in each.

    Q1. What is the probability that the number of red cards in pile A is the same as the number of black cards in pile B?

    Q2. How many cards would you have to turn over to see if that probability had transpired?

  • Joe

    12. You have two lengths of rope and a lighter. Each piece of rope has the property that, if lit at either end, it will take exactly one hour to burn completely. However, the burn rate is uneven across the length of each rope, and one rope is shorter than the other.

    How can you accurately measure 45 minutes?

  • Joe

    13. "The hardest logic puzzle ever"?

    Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

    Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god.

    The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.