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A cowboy walks into a bar and asks the barman for a glass of water. The barman pulls out a gun instead and points it at the man. The man genuinely says “Thank you” and walks out.
What happened?
The cowboy had hiccups and needed water. The barman shocked him with his gun instead and that cured the hiccups.
Three people check into a hotel room and each of them gets charged $10 – a total of $30. Later the clerk realizes that the bill is just $25, so he sends the bellboy to return $5 to the guests. On his way to the room, the bellboy decides to cheat and pockets $2 of the money, and gives the three men just one dollar each. Now the three men have spent $9 each, for a total of $27. Additionally, the bellboy took $2 for himself, which adds up to $27 + $2 = $29. Since the guests originally handed over $30, the question is what happened to the remaining $1?
The calculation is made the wrong way. The three men originally gave $30, but later $5 of them were sent back, which makes it $30 – 5 = $25 left at the clerk. Each of the men spent $9, so they gave $27 in total, $2 of which ended up in the bellboy’s pocket. $27 – $2 = $25, so no “missing dollar” here.
3 x $9 – $2 = $30 – $5.
Where is the driver sitting in this car?
Using the positioning of the mirrors, you can conclude that the driver is sitting on the right.
All integer numbers between 1 and 121 are written in the cells of a square grid with size 11 by 11. Then the product of the numbers in every row and the product of the numbers in every column are calculated. Is it possible that the set of all 11 column products coincides with the set of all 11 row-products?
No, it is not possible. There are 13 prime number between 61 and 121. Since there are only 11 rows, two of them, X and Y, appear in the same row. Now that row is divisible by XY, but clearly, no column is divisible by that number.
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.
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.
On top of which number is the car parked?
You are looking at the parking lot upside-down. The numbers on the picture are from 85 to 92. The car is parked on top of 87.
Which of the following objects below is the odd one?
The second square is the odd one – each of the others has some unique feature (shape, boundary, color, size), except for it.
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.
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”.
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