Twill #2 answer

The finished swatch

The weave: DDLDLL / LLDDLD / LDDLDL / DLLDLD / DDLLDL / LLDLDD (L = light, D = dark, each row from left to right, top row first). Every row and column has 3 of each thread, and no thread runs three in a row.

A easy swatch: Monday's puzzle. The hardest idea it needed was counting to half in a row or column.

How to crack it: the first moves

1. Two light threads sit side by side, so the square next to them (row 4, column 1) must be dark: never three in a row.
2. Two light threads sit side by side, so the square next to them (row 4, column 4) must be dark: never three in a row.
3. A gap between two dark threads must be light (row 4, column 5), or there would be three in a row.
4. Two light threads sit side by side, so the square next to them (row 1, column 1) must be dark: never three in a row.
5. Two dark threads sit side by side, so the square next to them (row 6, column 1) must be light: never three in a row.
6. Two light threads sit side by side, so the square next to them (row 3, column 5) must be dark: never three in a row.

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