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.
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.
Question: John has three daughters who are all unmarried. The youngest always lies, the oldest always tells the truth, and the one in the middle either tells the truth or lies. A very rich young man comes to John's house and says he wishes to marry one of his daughters. Naturally he wants to marry the oldest or the youngest so he will always know if she is lying or telling the truth. John agrees but says he can only ask one of the girls a yes or no question to decide which one he marries. They all look the same age.
What one question does he ask one of the daughters at random to figure out which daughter is the youngest or oldest?
Answer: "Is she older than her?" (He would ask one of the daughters if one of the other daughters is older than the last daughter). He always should pick the younger daughter based on what he knows. If he asks the older daughter and she says yes, then the youngest daughter will be known. If he asks the older daughter and she says no, then the youngest daughter is the other one. If he asks the youngest daughter and she says yes, she is lying and he will still pick the oldest. If he asks the youngest and she says no, he will just pick the other like in the first case. If he asks the middle daughter it doesn't matter because both will be acceptable choices.
Question: You have two coconuts and you want to find out how high they can be dropped from a 100 story building before they break. But you only have $1.40 and the elevator costs a dime each time you ride it up (it's free for rides down).
How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?
Note: They break when dropped from the same height and they don't weaken from getting dropped.
Answer: You could drop it at floor 1 first (because you start at floor 1). Then you would go to the floors: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, and 100. Whatever floor your first coconut breaks at, go to the floor above the last floor the coconut survived and drop the second coconut from this floor. Then go up by one floor until the second coconut breaks and that is the lowest floor it will break at.
Question: A man was born on January 1st, 23 B.C. and died January 2nd, 23 A.D. How old did he live to be?
Answer: 45 years old.
There is no year 0 so you can add 23 to 23 but you must subtract one to take year 0 out of consideration: 23 + 23 - 1 = 45 years old. In some cultures people are born 1 years old, in this case they would be 46 years old when they die.
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