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#1: Initial revision
by
Peter Taylor
·
2026-08-06T08:06:33Z (about 1 month ago)
```txt +---+---+---+---+ | | | 0 0 1 3 | + + | | | 1 1 0 3 | + + | | | 2 3 3 2 | + + | | | 3 2 2 1 | +---+---+---+---+ ``` <details><summary>Step 1</summary> The `3` in the bottom-left must be with one of the `2`s next to it, so we can separate every other `2-3` boundary: ```txt +---+---+---+---+ | | | 0 0 1 3 | + + | | | 1 1 0 3 | + +---+ | | | | 2 3 3 | 2 | + +---+ + | | | 3 2 2 1 | +---+---+---+---+ ``` </details> <details><summary>Step 2</summary> Then starting from the `2` on the right edge we have three forced dominos due to cells with only one available neighbour: ```txt +---+---+---+---+ | | | 0 0 1 3 | + + | | | 1 1 0 3 | +---+ +---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` </details> <details><summary>Step 3</summary> If there's a `3-3` at the top-right then we force the other `3-3` to split up: ```txt +---+---+---+---+ | | | | 0 0 1 | 3 | + +---+---+ + | | | | | | 1 | 1 | 0 | 3 | +---+ + +---+ | | | | | | 2 | 3 | 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` and we end up with two `0-1`s in the top-left. Therefore we split the `3-3` in the top-right: ```txt +---+---+---+---+ | | | | 0 0 | 1 3 | + +---+---+ | | | | 1 1 | 0 3 | +---+ +---+---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` </details> <details><summary>Step 4</summary> This forces the other `3-3` and the top-left square can only form distinct dominos in one way: ```txt +---+---+---+---+ | | | | 0 0 | 1 3 | +---+---+---+---+ | | | | 1 1 | 0 3 | +---+---+---+---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` </details> Alternatively, <details><summary>Step 3 alternate</summary> If we split the `0-0` in the top-left then the leftmost one forms a `0-1` and the rightmost one would also form a `0-1` whichever remaining neighbour it takes: ```txt +---+---+---+---+ | | | | 0 | 0 1 3 | + + + | | | | 1 | 1 0 3 | +---+ +---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` Therefore the `0-0` is forced: ```txt +---+---+---+---+ | | | | 0 0 | 1 3 | +---+---+ + | | | 1 1 0 3 | +---+ +---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` </details> <details><summary>Step 4 alternate</summary> This forces a chain of two more dominos through cells with only one available neighbour: ```txt +---+---+---+---+ | | | | 0 0 | 1 3 | +---+---+ + | | | | 1 1 | 0 3 | +---+---+---+---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` </details> <details><summary>Step 5 alternate</summary> Since we now have a `3-3` we must split the `3-3` in the top-right, completing the solution: ```txt +---+---+---+---+ | | | | 0 0 | 1 3 | +---+---+---+---+ | | | | 1 1 | 0 3 | +---+---+---+---+ | | | | | 2 | 3 3 | 2 | + +---+---+ + | | | | | 3 | 2 2 | 1 | +---+---+---+---+ ``` </details>