I just learned with sadness that John Conway has died two days ago, on April 11, of Covid-19. I am in no position to write an obituary. His playful creativity led to a synthesis of simplicity and depth that I will always gratefully admire.
I like puzzles with few pieces, as the readers of this blog know.
Here is such a puzzle with just one puzzle piece, which comes with its mirror image. I suggest to print the template below, cut along the fat lines, and fold & glue the diamonds into triangles. This will give you six identical triangles that you can flip over to get the mirror symmetric version. I will explain later how this puzzle piece came into existence.
We are going to use this tile according to timely rules: We may put two triangles together along an entire edge if the colors nowhere match along the edge:
This is a strong limitation, but we can still use this puzzle piece to tile larger triangles, like so:
Do you think you can tile even larger triangles? Try it!
Below is a more interesting puzzle. I have been trying to tile the hexagonal ring, but failed, as there is no way to place the puzzle piece into the remaining gap. Can you find a solution that closes up and doesn’t violate the rules?
Then you can make your own challenges: Print a game board with triangles as below, and place randomly two of the puzzle pieces onto it. Can you form a chain that (legally and ethically) connects the two triangles? Below is a very simple example with solution.
Here are two more puzzles. At least one of them is harder than you probably like. But who knows.
A slightly cryptic hint about what is going on here is below. Stay safe.
The Inner Frame 