Lab Mice

A scientist has 9 bottles, exactly one of which contains poison. The poison kills any creature which drinks it within 24 hours. If the scientist has 2 lab mice at his disposal, how can he find which is the poisonous bottle within 2 days only?

Label the bottles B1, B2, B3, … , B9.
The first day he lets the first mouse drink B1, B2, B3, and let the second mouse drink B1, B4, and B5. If after 24 hours both mice die, then the poisonous bottle is B1. If only one mouse dies, say the first one, then he lets the second mouse drink B2. If it dies, then the poisonous bottle is B2, otherwise, it is B3. Finally, if neither mouse dies, then he lets the first mouse drink B6 and B7, and lets the second mouse drink B6 and B8. If both mice die after 24 hours, then the poisonous bottle is B6. If only one mouse dies, say the first one, then the poisonous bottle is B7. If neither mouse dies, then the poisonous bottle is B9.

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Y-Town

In Y-town all crossroads are Y-shaped, and there are no dead-end roads. Is it true that if you start from any point in the city and start walking along the roads, turning alternatingly left and right at each crossroad, eventually you will arrive at the same spot?

Yes, it is true. If you start walking forward, eventually you will end up in a loop. It is easy to see that your entire path, including the starting spot, must belong to this loop. Therefore, eventually you will end up in the starting spot again.

Reverse Puzzling

George is a great puzzler, so I was extremely surprised when he didn’t immediately know the answer to a really famous puzzle. It’s a puzzle that you probably did years ago, and have heard so often you can do it from memory rather than working it out. It’s also not really that difficult, so I was also surprised when it appeared to be stumping him.

“Come on, surely you know this one,” I said.

“I don’t. And don’t call me Shirley.” He answered grumpily. I could tell his mood was declining rapidly, but like any great puzzler he was down and not out, and I watched his facial expression change as he reached into his mental bag of tricks. He nodded towards a conveniently located whiteboard. “Have you got a marker for that?”

I handed him one, and he drew up the following diagram:

He stepped back, admiring his work, beaming proudly. “Well, now the solution is very obvious!” he commented. And indeed it was. The question for you is:

What is the puzzle?

The diagram represents the puzzle about the man, trying to cross the river with a fox (F), a chicken (C) and a sack of barley (B). He can carry at most one of them with himself in the boat, and he shouldn’t leave the chicken alone with the fox or with the barley on one side of the river. The red dots represent all admissable configurations and the lines between them all available moves.

Source:

Puzzling StackExchange

Athletics Competition

An athletics competition, organized periodically, rewards a medal to 79 winners, 47 runner-ups, and an indeterminate number of third places. If 50 cans of drink are served for refreshment, how many policemen are needed to keep order?

The numbers are references to elements in the periodic table. 79 is the number of Gold, 47 is the number of Silver, 50 is the number of Tin, and Bronze is not in the periodic table. Since 29 is the number of Copper, it should be the correct answer.

Source:

Puzzling StackExchange

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100 Hats and 1 Million Dollars

A challenge is given to 100 people. A hat will be placed on each of their heads, and each hat will have an integer between 1 and 100 written on it (numbers can repeat). Every person will be able to see the hats of the other 99, but not his own. After that, everyone will have to guess what is the number on their hat (without others hearing). If at least one person guesses correctly, they will be awarded 1 million dollars. What strategy should the people come up with in order to optimize their chance of winning?

Label the people with numbers 1, 2, 3, … , 100. A strategy which ensures 100% success is the following:
Person X should sum the numbers on the hats of the other 99 people, then subtract the result from X, and take the residue modulo 100 of the answer (say “100” if the residue is 0).
This way if the sum of the numbers on all hats has residue R when divided by 100, then person R will guess correctly the number on his hat.

Yes, No, I Don’t Know

Your friend is thinking of a number among 1, 2, and 3. You can ask him just one question, to which he is allowed to answer only with “yes”, “no”, or “I don’t know”. What would you ask him in order to find his number?

You can ask him the following:

“If I am thinking of a number among 1 and 2, is your number going to be bigger than mine?”

If your friend’s number is 1, he will say “no”. If his number is 2, he will say “I don’t know”. If his number is 3, he will say “yes”.