In Memoriam (Solitaire V)

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.Pieces

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.

 

Template

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:Rules

This is a strong limitation, but we can still use this puzzle piece to tile larger triangles, like so:

Triangles

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?

Hexring

 

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.

Pathpuzzle1

Here are two more puzzles. At least one of them is harder than you probably like. But who knows.

Pathpuzzle2

A slightly cryptic hint about what is going on here is below. Stay safe.

Connected

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