Twill #7 answer

The finished swatch

The weave: LDDLDLDL / DDLDLDLL / LLDLDLDD / LLDLDDLD / DDLDLDLL / DDLLDLDL / LLDDLLDD / DLLDLDLD (L = light, D = dark, each row from left to right, top row first). Every row and column has 4 of each thread, and no thread runs three in a row.

A hard swatch: Saturday's puzzle. The hardest idea it needed was trying every way to finish a row or column.

How to crack it: the first moves

1. A tie (=) joins two squares of the same thread, so this one (row 4, column 1) is light too.
2. Two light threads sit side by side, so the square next to them (row 4, column 3) must be dark: never three in a row.
3. A tie (=) joins two squares of the same thread, so this one (row 3, column 1) is light too.
4. Two light threads sit side by side, so the square next to them (row 2, column 1) must be dark: never three in a row.
5. Two light threads sit side by side, so the square next to them (row 5, column 1) must be dark: never three in a row.
6. A tie (=) joins two squares of the same thread, so this one (row 2, column 2) is dark too.

Every Twill swatch can be woven this way, one deduction at a time, without guessing.