Earlier today I set you the following puzzle:
Here’s a square divided into eight segments, and the four ‘mirror lines’ of that square. In other words, you can reflect the square across each axis and the square looks exactly the same.
If we colour the top two segments green, as below, and leave the rest white, the square now only has a single mirror line, the vertical one:
How many different ways can you colour the square with two colours such that
1. The only mirror line is the horizontal mirror line?
2. The only mirror line is the right-sloping diagonal mirror?
3. The square has both horizontal and vertical mirror lines, but no diagonal mirror lines?
4. The square has a diagonal mirror line and a horizontal mirror line, but not a vertical mirror line?
Solutions:
1. 6 ways.
2. 6 ways
3. 1 way.
4. 0 ways. Combining a diagonal mirror reflection with a horizontal mirror reflection leads to a vertical mirror reflection.
UPDATE: This article has been corrected after readers pointed out an error. There are 6 solutions for Q2 not 5 as previously stated. Sorry for the mistake.
Thanks again to Alex Berke for today’s puzzle. Her book is Beautiful Symmetry: A Coloring Book About Math.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
