May 30, 2024


Apologies to any Antipodean Swifties arriving on this page. Today’s puzzle is about tiles, and whether or not you can solve them quickly.

The puzzle involves black and white tiles on a 4×4 grid. Consider the image below, which highlights adjacent rows in the grid.

For each cell in a top row, there are two choices for the cell directly below it: either it has the same color, or it has a different color.

For example, in the checkerboard pattern, lower left, each tile in the top row has a tile of a different color below it. Similarly for row 2 and row 3.

For the grid on the right, two of the top row of tiles have a different color directly below them, and two have the same color directly below them. For the second row, again, two have a different color under them, and two the same color. However, the pattern breaks down in the third row, where all four tiles have a different color underneath them.

Project tile

Your task is to find a way to tile the grid such that:

1) For each row (except the bottom one), two tiles have the same color directly below them and two tiles have a different color.

2) For each pair of adjacent columns, (shown below) two tiles in the left column have the same color directly to the right and two tiles in the left column have a different color to the right.

If you found it easy, here’s one for the pros: can you tile an 8×8 belt the same way? That is, such that for every pair of adjacent rows/columns that match, the tiles match in half the positions and differ in half the positions?

I’ll be back with a fix at 5pm UK.

NO SPOILERS Please discuss your favorite tiles, Tylers, Taylors and/or windswepts instead.

Today’s puzzle was devised by maths outreach legends Katie Steckles and Peter Rowlett, who along with Sam Hartburn and Alison Kiddle are the authors of Shortcuts: Mathematics, which provide bite-sized introductions to many mathematical ideas. One topic included is matrices and block designs, an introduction to these is this puzzle.

Katie and Peter are also both part of Finite Group: an online community for people interested in playing with mathematical ideas – with monthly live streams and discussions, as well as a stream of interesting math content from all over the internet. Visit patreon.com/finitegroup to report.



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