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A paper version of the Seven Triples puzzle

Last year I wrote about a 3D-printed puzzle I’d designed, called Seven Triples.

At work we want to use this puzzle during an A-Level enrichment day, which means we need about twenty copies of it. I 3D-printed four copies over the course of a couple of weeks, in amongst other jobs, and I don’t have the patience to do any more. So, I’ve made a 2D version that we can print and cut out much more quickly.

Triangles arranged in rows. Each triangle is filled with one of seven patterns. There are white, yellow and magenta triangles.

I didn’t fancy cutting out a load of circles, so the pieces are now 120°-30°-30° triangles. You can fit three pieces together to make a big equilateral triangle.

There are still seven kinds of piece, with three colours of each. I went with abstract shapes again, so that one of the first steps in finding a solution is giving names to each kind of piece. The patterns are designed to be easy to distinguish at a glance.

We have our own poster printer, and apparently more A1 canvas than anyone knows what to do with, so I printed a single A1 sheet containing twelve full sets of pieces. I chose pure magenta and pure yellow for the coloured pieces, so we could directly measure how much ink was used.

Printed A1 sheet lying on a table. Triangle pieces are arranged in rows. There are six rows each of white, yellow and magenta triangles.

It took just under an hour to cut it all out!

Cutting out the triangles

The canvas should be more durable than paper, but it’s still quite floppy. We’ll find out if I should’ve stuck it onto something more firm when the first lot of kids try it. I’m also unsure how the ink will hold up to hard use by mucky hands.

This is a lovely puzzle, so I’m happy to share it. We had a good think about how best to state the aim. Here’s what we came up with, as a series of prompts:

  • (Give each group a full set of pieces – 21 triangles, comprising three colours of each of the seven patterns)
  • Can you arrange the pieces into seven groups so that all the pieces in each group are different colours?
  • Now, can you rearrange the pieces so that all the pieces in each group have a different pattern, as well?
  • Finally, can you arrange the pieces so that no pair of patterns appears in more than one group? For example, if you’ve got polka dots and stripes in one group, no other group should have both polka dots and stripes.

Here are a few printable sheets of pieces, in different sizes and either colour or black and white:

And finally, here’s the SVG file in case you want to change the colours:

(will not be published)

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