You have a large number of friends coming over and they all get thirsty. Your first friend asks for 1/2 a cup of water. Your second friend asks for 1/4 a cup of water. Your third friend asks for 1/8 a cup of water, etc.
How many cups of water do you need to serve your friends?
Answer: Just one. If your friends kept asking for water like this forever one cup would be enough.
John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
Answer: 301 eggs. The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
Question: Queens can move horizontally, vertically and diagonally any number of spaces as illustrated. One piece 'attacks' another if it moves to the same tile that the other piece is on. How can you arrange eight queens on the board so they cannot attack each other?
Hint: Four must go on black and four on white.
Answer: Here are the two solutions. This is usually solved with guess and check although using logic may be faster. We know that each queen must be in it's own row vertically and horizontally. We also know that 4 of the queens must be on white and 4 on black. This is true because with 4 queens on the same color all of the rest of that color is venerable to attack. (It could be done with math).
Question: In an apartment complex in New York there are one hundred married couples. When one of the husbands cheats on his wife with one of the other wives, his wife has no idea. With the large amount of gossip in the complex, all of the other wives know he is cheating. If a wife finds out that her husband is cheating on her, she kills him the following morning. Someone anonymously sends an email to all of the wives in the building saying that at least 1 man is cheating on his wife in the building.
How many husbands will be killed and how long will it take?
Answer: All of the men (n) who are cheating will be killed and it will take one less than the number of cheating men nights (n-1) for their wives to discover this.
If one man was cheating, and that woman hadn't have heard of any other infidelity she would know it was her husband that was cheating. If there was two men cheating, both of their wives would think that since they have only heard of one man cheating he should die the next morning. If he doesn't die, she knows her husband must also be cheating and that's why the other husband didn't die. Following this logic, you can know that all of the men will die after one less night than there is cheating men.
Question: Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails. What is a fair way for the men to toss the coin and decide who gets the coin?
Answer: They just have to flip it twice. They call the first toss either heads or tails, then the next toss they automatically pick the opposite (ie if one man calls heads on the first flip, he automatically picks tails on the second and vice versa). If they both win one toss (a tie) out of the two, they just have to repeat until one of them wins both tosses.
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