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Can you solve it? Tiler swift | Can you solve it? Tiler swift |
(about 11 hours later) | |
The tortured puzzlers department | The tortured puzzlers department |
UPDATE: Read the solution here | |
Apologies to any Antipodean Swifties arriving on this page. Today’s puzzle is about tiles, and whether or not you can solve it swiftly. | Apologies to any Antipodean Swifties arriving on this page. Today’s puzzle is about tiles, and whether or not you can solve it swiftly. |
The puzzle concerns black and white tiles on a 4x4 grid. Consider the image below, which highlights adjacent rows in the grid. | The puzzle concerns black and white tiles on a 4x4 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 colour, or it has a different colour. | For each cell in a top row, there are two choices for the cell directly below it: either it has the same colour, or it has a different colour. |
For example, in the checkerboard pattern, below left, each tile in the top row has a tile in a different colour below it. Likewise for row 2 and row 3. | For example, in the checkerboard pattern, below left, each tile in the top row has a tile in a different colour below it. Likewise for row 2 and row 3. |
For the grid on the right, two of the top row tiles have a different colour directly below them, and two have the same colour directly below them. For the second row, again, two have a different colour below them, and two the same colour. The pattern breaks down, however, in the third row, where all four tiles have a different colour below them. | For the grid on the right, two of the top row tiles have a different colour directly below them, and two have the same colour directly below them. For the second row, again, two have a different colour below them, and two the same colour. The pattern breaks down, however, in the third row, where all four tiles have a different colour below them. |
Project tile | Project tile |
Your task is to find a way to tile the grid such that: | Your task is to find a way to tile the grid such that: |
1) For every row (except the bottom one), two tiles have the same colour directly below them and two tiles have a different colour. | 1) For every row (except the bottom one), two tiles have the same colour directly below them and two tiles have a different colour. |
2) For every pair of adjacent columns, (shown below) two tiles in the left column have the same colour directly to the right and two tiles in the left column have a different colour to the right. | 2) For every pair of adjacent columns, (shown below) two tiles in the left column have the same colour directly to the right and two tiles in the left column have a different colour to the right. |
If you found that easy, here’s one for the pros: can you tile an 8x8 gird the same way? That is, such that for each pair of adjacent rows/columns matches, the tiles match in half the positions and differ in half of the positions? | If you found that easy, here’s one for the pros: can you tile an 8x8 gird the same way? That is, such that for each pair of adjacent rows/columns matches, the tiles match in half the positions and differ in half of the positions? |
I’ll be back with a solutions at 5pm UK. | I’ll be back with a solutions at 5pm UK. |
NO SPOILERS Please discuss your favourite tilers, Tylers, Taylors and/or swifts instead. | NO SPOILERS Please discuss your favourite tilers, Tylers, Taylors and/or swifts instead. |
Today’s puzzle was devised by maths outreach legends Katie Steckles and Peter Rowlett, who together with Sam Hartburn and Alison Kiddle are the authors of Short Cuts: Maths, which provides bite-sized introductions to many mathematical ideas. One topic included is matrices and block designs, an introduction to which is this very puzzle. | Today’s puzzle was devised by maths outreach legends Katie Steckles and Peter Rowlett, who together with Sam Hartburn and Alison Kiddle are the authors of Short Cuts: Maths, which provides bite-sized introductions to many mathematical ideas. One topic included is matrices and block designs, an introduction to which is this very puzzle. |
Katie and Peter are also both part of Finite Group: an online community for people interested in playing with mathematical ideas - with monthly livestreams and discussion, as well as a feed of interesting maths content from all over the internet. Visit patreon.com/finitegroup to sign up. | Katie and Peter are also both part of Finite Group: an online community for people interested in playing with mathematical ideas - with monthly livestreams and discussion, as well as a feed of interesting maths content from all over the internet. Visit patreon.com/finitegroup to sign up. |
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