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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.
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.
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.
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.
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.
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.
You are sitting in a motionless car, which is tightly sealed, i.e. no open windows, holes in the car, etc. A helium balloon on a string is tied to the floor. If you start accelerating the car, is the balloon going to move back, forward, or stay in place?
The reason the balloon floats up in the air is that the helium has a lower density, so when gravity pulls the denser air around down, the balloon gets pushed up. Similarly, when the car accelerates, the air around gets drawn to the back of the car, which makes the helium balloon go forward.
Two moms, Sarah and Courtney, are talking to each other.
Sarah: I have two children
What is the probability that both of Sarah’s children are boys?
Courtney: Me too! Do
What is the probability that both of Courtney’s children are boys?
Sarah: Yes, I do! What is your younger child?
What is the probability that both of Sarah’s children are boys?
Courtney: It is a boy. He is so mischievous!
What is the probability that both of Courtney’s children are boys?
Sarah: Is he Sagittarius? Sagittarius boys are known to drive their mothers crazy. I can testify from personal experience.
What is the probability that both of Sarah’s children are boys?
Courtney: No, but actually I have the opposite personal experience to yours.
What is the probability that both of Courtney’s children are boys?
Sarah: Well, I guess astrology does not always get it right.
Courtney: I assume it does about half of the time.
The answers are: ~1/4, ~1/4, ~1/3, ~1/2, ~23/47, 1.
Explanation:
Initially, we do not have any information about the children and therefore the chance that both of them boys is 1/2 × 1/2. This applies to the first and the second question.
After Sarah says that she has at least one boy, there are equal possibilities that she has Boy + Boy, Boy + Girl, or Girl + Boy. Therefore, the chance that both children are boys is 1/3.
After Courtney says that her younger child is a boy, the only remaining question is what is the gender of her older child, and therefore the chance is 1/2.
The fifth exchange implies that Sarah has a Sagittarius boy. There are 23 combinations such that both children are boys and at least one of them is Sagittarius. There are 47 combinations such that at least one of the children is a Sagittarius boy. Therefore, the chance that both children are boys is 23/47.
Finally, Courtney says that her younger child, which is a boy, is not Sagittarius, but her personal experience with Sagittarius boys is positive. Therefore, her older child is a Sagittarius boy and the chance is 1.
I give you a pen and paper and ask you to write the numbers from 1 to 100 in succession so that there are no three numbers such that twice the second one is equal to the sum of the first and the third one. The three numbers do not need to be successive in the sequence.
Remark: The sequence 3, 1, 2, 5, 4 works, but the sequence 1, 4, 2, 5, 3 does not because of the numbers 1, 2, and 3.
Start with the following sequences:
1 → 1, 2 → 2, 4, 1, 3 → 4, 8, 2, 6, 3, 7, 1, 5 → 8, 16, 4, 12, 6, 14, 2, 10, 7, 15, 3, 11, 5, 13, 1, 9
and keep iterating until you get a sequence with all numbers from 1 to 128. On each step you take the previous sequence, multiply all elements by 2, and then add the same result but with all elements decreased by 1. This will ensure that the first half contains only even numbers and the second half contains only odd numbers. Since the sum of an odd and an even number is not divisible by 2, if some sequence violates the property, then the previous sequence would have violated it as well.
Once you construct a sequence with 128 numbers, simply remove the numbers from 101 to 128 and you are done. To speed up the process, you can reduce the sequence 8, 16, 4, 12, 6, 14, 2, 10, 7, 15, 3, 11, 5, 13, 1, 9 to 8, 4, 12, 6, 2, 10, 7, 3, 11, 5, 13, 1, 9 and then continue the process.
One person went to the store and bought groceries for $13.59 total. He paid with a $100 bill, took his change, and left the store. There was something special about this transaction. What is it?
The person paid with a $100 bill. The cashier returned him a $50 bill, a $20 bill, a $10 bill, a $5 bill, a $1 bill, a quarter, a dime, a nickel, and a cent. The transaction consisted of exactly one of each (frequently used) denominations.
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