Thread:BunsenH/@comment-25404524-20161021034513/@comment-24577221-20161031004945

For example, here's a math-related puzzle with a "trick".

Suppose you start with an island with an empty 8 x 8 square. It has 64 spaces.



Next, suppose you buy 32 Wild Bagpipes. Each takes a 1 x 2 area — that is, a total of 64 spaces, in pairs.



It is fairly easy to pack all 32 Wild Bagpipes into the square. In fact, there are many ways of doing it. (It would be difficult to figure out how many, or to list them all! But that's not what I'm going for here.)



You can try this yourself, using a checker board or chess board and something that can mark the squares in pairs. Dominoes would work nicely, or Lego pieces; whatever you have on hand.

BUT. Suppose you fill in two opposite corners of the square, leaving just 62 spaces.



The question: Can you fill in the rest of the square with 31 Wild Bagpipes? They would take up 62 spaces.

Or, can you prove that it is impossible to do?

There are a number of math problems which come down to: Can you find a solution, or can you prove that no solution is possible?

If you want to try to answer this, I really do suggest that you work with a checker board or chess board.

Have fun!