Math Riddles

Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

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?

Question: 2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes?

Question: The warden of a circular jail is extremely hyper one day so he begins running around opening cells. The jail has 100 cells numbered from 1 to 100. He runs in a circle and opens all of the cells. Next he runs around and closes every 2nd cell (starting with cell 2, 4, 6 , etc.). If a cell is open he closes it and if a cell is closed he opens it. When he finishes running by all 100 cells he opens/closes every 3rd cell (starting with 3, 6, 9, 12 etc.), then every 4th cell (starting with 4, 8, 12, etc.) and so on. He does this until he goes around and only changes the 100th cell.

When he is done what cells will be open?

Question: You create your own Where's Waldo game on a piece of paper. You want your friend to find Waldo but they think you might be pulling a prank on them by not putting Waldo on the paper at all.

How can you prove to your friend that Waldo is on the paper without ruining it for them?