Math Riddles

Question: If you have 30 white socks, 22 black socks, and 14 blue socks scattered across the floor in the dark, how many would you have to grab to get a matching pair?

Question: Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself. Each guest got $1 back: so now each guest only paid $9; bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?

Question: A man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are. The mathematician says "I have three daughters and the product of their ages is 72." The man tells the mathematician that he needs more information, so the mathematician tells him "The sum of their ages is equal to our apartment number." The man still needs more information so the mathematician tells him "My oldest daughter has her own bed and the other two share bunk beds."

How old are his daughters?

Question:

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?

Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others is bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?