Twill #4 answer

The finished swatch

The weave: LLDDLD / LLDDLD / DDLLDL / DLLDDL / LDDLLD / DDLLDL (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 medium swatch: Wednesday'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. Try every way to finish row 3 (half of each thread, never three in a row, its ties and crosses). Every one of them makes this square (row 3, column 4) light.
2. A cross (x) joins two different threads, so this one (row 4, column 4) is dark.
3. A tie (=) joins two squares of the same thread, so this one (row 4, column 5) is dark too.
4. Two dark threads sit side by side, so the square next to them (row 4, column 3) must be light: never three in a row.
5. Two dark threads sit side by side, so the square next to them (row 4, column 6) must be light: never three in a row.
6. Two dark threads sit side by side, so the square next to them (row 2, column 5) must be light: never three in a row.

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