Here are a few puzzles with simple and thematically similar solutions. They require no math and are accessible to layfolk. I included sources where I could.
Save the World
Aliens have invaded and chosen you and 9 other people to determine the fate of the world. You can strategize beforehand.
- Each person is given a hat, red or blue.
- Person n can see the colors of hats 1, 2, 3, … n - 1 (but not their own). So, person 1 sees nothing!
- In reverse order, beginning with person 10, each person guesses the color of their hat. Everyone can hear what each person guesses.
- People can only say “red” or “blue.” They cannot communicate to each other using pronunciation, speed, etc.
- At the end, for each wrong guess, the aliens kill 10% of Earth’s population.
What is the maximum percentage of humanity that can be guaranteed to be saved?
Mutilated Chessboard (source, with solution)
A standard 8 by 8 chessboard has the lower left corner and the upper right removed, with the remaining 62 squares left intact. You are given 31 dominoes, each of which can cover 2 squares.
- The dominoes may be oriented vertically or horizontally.
- The dominoes may not overlap or go off the edge of the board.
Can you cover the chessboard with the dominoes?
Purple and Orange Polyhedra (source: 2013 HCSSiM Interesting Test)
I have a bin of containing purple and orange plastic polyhedra, 2013 of each. I have plenty of additional polyhedra of both colors, so I won’t run out. Every 17 seconds, I remove two polyhedra at random from the bin.
- If they are the same color, I put a purple polyhedron into the bin.
- If they are different colors, I put an orange polyhedron into the bin.
When there is only one polyhedron left in the bin, what is the probability that it is orange?
Chocolate Bar
You have an n by m rectangular Hershey’s bar, and you want to break it up according to the grid (i.e., in the usual way) to get n*m pieces.
- You can only break one piece at a time; you may not do things like stacking multiple pieces on top of each other and then breaking them.
