Marin Math Circle will be restarting in Spring 2017. If you haven’t already done so, you are welcome to register for updates as we prepare. Thank you for your continued support of MMC.

If you would like to receive updates about the program, please subscribe to the Marin Math Circle google group. To join, go to https://groups.google.com and search for “Marin Math Circle.”

Below are a few puzzles, and here are some more problems.

There are 100 light switches on the wall, all turned off. A hundred toddlers come by. The first toddler flips every switch. Then the second toddler flips just switches 2, 4, 6, 8, … etc. Then the third toddler flips switches 3, 6, 9, 12, … etc. This pattern continues until finally the 100th toddler flips just switch number 100. How may lights are turned on at the end?

A military base has a number of identical hoverplanes. Each hoverplane can carry enough fuel to fly exactly halfway around the planet. Hoverplanes do not use any fuel while hovering stationary in the air, and hoverplanes can transfer any amount of fuel between each other while in the air. What is the minimum number of planes are that are needed so that one plane is able to get all the way around the planet and all assisting planes return safely to base?

What is the maximum number of pieces you can divide a watermelon into with four straight cuts, if you are NOT allowed to rearrange the pieces between cuts? With five cuts?