Question: You have a cup of tea (A) and a cup of coffee (B) (equal amounts), and you take a spoonful of the coffee (B) and mix it thoroughly into the tea (A). Then you take a spoonful of tea (A) and mix it with the coffee (B). Does the cup that originally had tea in it (A) have more coffee or does the cup that originally had coffee in it (B) have more tea?
Answer: Both cups end up having the same amount of the other liquid in it. When you take the spoonful of coffee (B) and put it in the tea (A) it increases the volume of the tea (A) by that spoonful. Then when you take a spoonful of the tea (A), part of that spoonful is coffee, taking away the proportional amount of coffee. This makes the amount of coffee in the tea and tea in the coffee equal.
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: My first is often at the front door.
My second is found in the cereal family.
My third is what most people want.
My whole is one of the united states.
What am I?
Answer: Matrimony (mat rye money). Which is certainly a united state!
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: 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.
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