July 21, 2024

Today’s puzzles are of a piece. Two, three and five pieces, to be exact.

In each problem you are given a set of non-symmetrical shapes. The challenge is to rearrange them without overlaps so that the combined shape has a line of symmetry.

1. Triangular twins

An easy one to start. These two ’30-60-90′ triangles share a side length.

(Each triangle has internal angles of 30, 60 and 90 degrees: what you would get if you cut an equilateral triangle in half.)

How would you rearrange the two triangles without overlaps to get a shape with mirror symmetry, that is, one in which a line divides the shape into two halves, one half the reflection of the other.

Find BOTH solutions.

2. Tetromino triplets

This one for the tetris fans. Here are three L-shaped tetrominos (the technical term for a shape made of four squares connected along grid lines.)

Can you rearrange them without overlapping so that the combined shape has a line of mirror symmetry?

There is one way to do it without flipping, and one way with flipping. (Imagine you have cut out the shapes. There is one solution just by moving the shapes around, and one way in you have to pick up one shape and turn it over before putting it back on the table.)

3. Triomino quintuplets

The same again, this time with five L-triominoes (ie a shape made of three squares.) Can you rearrange them without overlapping so that the combined shape has a line of mirror symmetry?

The most entertaining (and useful) way to solve these problems is to cut them out of paper and do the rearrangement by hand.

However, if someone wants to make an interactive version, I’m sure all fellow readers would appreciate it. Post the link in the comments below, and I’ll add it here.

I’ll be back at 5pm UK with the solutions. PLEASE NO SPOILERS. Instead, discuss early computer games, or your favorite tetrominos.

Today’s puzzles were devised by Donald Bell, former director of the National Engineering Laboratory. If you want to hear more about his passion for polyominoes, here is a speech he gave about them.

I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.

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