If you are new, start with how to play Twill. This guide assumes you know the rules: half light and half dark in every row and column, never three of a thread side by side, ties (=) for the same thread and crosses (x) for different ones, and on Sundays no two rows or columns alike. Below, L is light, D is dark, a dot is an empty square, and squares are named row first, then column.
What each day asks of you
Our solver grades every swatch by the ideas it needs. Easy 6x6 swatches keep at least ten woven squares and need only pairs, gaps and counting. Medium 6x6 swatches must need the finish-the-line idea at least three times, and lean on ties and crosses at least three times. Hard 8x8 swatches need finishing a line at least four times and may need up to two short what-ifs, each no more than five moves long. Sunday swatches are like Hard ones but must also use the no-twins rule at least twice. Harder swatches can start almost bare: Twill No. 6 (Friday 30 October) began with a single woven square and seventeen ties and crosses, so the links are the puzzle.
Ties and crosses as chains
A tie or cross next to a woven square settles its partner, and that is the easy part. The more useful habit is to read links as chains before any thread is known.
- A tie then a cross: if A = B and B x C, then A and C are different. Two crosses in a row make the ends the same.
- A tie between two neighbours in a line makes them a pair, whatever the thread. The squares either side of that pair must both be the other thread, so they match each other.
- A cross between two neighbours always gives the line one light and one dark. For counting, you can treat those two squares as already done.
- A row of six with two crossed pairs in it has its other two squares as one of each too, since the crossed pairs supply two light and two dark.
Counting, the quick way
Counting is the second idea in our solver: once a line has half of one thread, the rest is the other. On an 8x8, a line with four of one thread is finished in one move. The trap is a line that is one short: three light in an eight-square row tells you nothing by itself, but if two of its gaps are joined by a cross (so they hold one light between them), every other gap must be dark.
Finishing a line in your head
This is the idea Medium swatches are built around: take one row or column, list every way to finish it that keeps half of each thread, avoids three in a row and obeys the ties and crosses inside that line, and see whether they all agree on some square. It sounds heavy, but lines are short. There are only 14 ways to weave a valid row of six, and 34 for a row of eight, so a line with a few squares known usually has just two or three ways left.
Two patterns worth knowing by heart
- Same thread at both ends of a six: L . . . . L. The second and fifth squares must be D. If the second were L, the row would already hold three L (first, second and sixth), so the third, fourth and fifth would all be D: three in a row. The same argument works from the other end.
- L . . . L . (light in the first and fifth squares of a six): the sixth square is D. If it were L, the row would have three L already, leaving the second, third and fourth all D, which is three in a row.
A real example: Twill No. 4
Twill No. 4 (a Medium from Wednesday 28 October) opens with this idea. Row 3 has only one woven square, D in column 5, plus a tie joining columns 1 and 2. Suppose column 4 were D. Then columns 4 and 5 form a dark pair, so columns 3 and 6 must be L. That gives two of each so far, and the tied pair in columns 1 and 2 must supply one L and one D, which a tie forbids. So column 4 is L. Checking both remaining finishes (L L D L D D and D D L L D L) confirms it, and the second is the one the swatch ends with. You can see the full weave on the Twill No. 4 answer page.
Sunday: no twins
On twill day no two rows may be woven the same, and no two columns. The rule only bites when a line is nearly finished and one of its possible finishes copies a line that is already complete. So the habit is: whenever a line is down to two gaps that must be one of each, compare both finishes with every finished line running the same way.
Twill No. 1 (Sunday 25 October) shows it. Late in the solve, column 8 read L, L, D, gap, gap, D, L, D from the top. Rows 4 and 5 needed one light and one dark, and both orders avoid three in a row, so the line alone could not decide. But column 2 was already finished as L, L, D, D, L, D, L, D, which is exactly what column 8 would become with D in row 4 and L in row 5. That copy is not allowed, so row 4 of column 8 is L and row 5 is D.
What if: a short test, done properly
On Hard days and Sundays the solver may need a what-if, and it limits itself to the moves a person can chase in their head: pairs, gaps, ties, crosses and counting, nothing cleverer. It only ever asks for two per swatch, each at most five moves long including the first. So when you try one, keep it short and stop the moment a rule breaks.
Here is the one from Twill No. 6. With much of the bottom half woven, the square in row 3, column 6 was still open. Imagine it light. Row 3 column 7 is already light, so that is a light pair and row 3 column 5 must be dark (the cross between columns 5 and 6 of row 3 says the same). In column 5, rows 3 and 4 are now both dark, so row 2 column 5 must be light. In column 6, rows 3 and 4 are both light, so row 2 column 6 must be dark. But a tie joins row 2 columns 5 and 6, and they have just come out different. Four moves, one broken rule: row 3 column 6 is dark. Full solution on the Twill No. 6 answer page.
Choosing where to test
- Pick a square with a link and a woven neighbour, so the first move sets off a pair or a tie straight away.
- Prefer squares next to a nearly full line, where one more thread triggers a count.
- Follow only forced moves. If nothing breaks within about five moves, rub it out and pick another square: our solver never needed a longer chain on a published swatch.
Quick checklist
- Sweep every row and column for pairs and gaps, then follow every tie and cross from a woven square.
- Read links as chains, and count crossed pairs as one of each.
- Count each line after every few moves; a line at half is finished.
- On Medium and above, pick lines with three or more squares known and list their finishes.
- On Sundays, compare nearly finished lines with finished ones running the same way.
- Use a what-if last, keep it under five moves, and test squares with links first.
Put it to work on today's Twill, or browse the Twill answers archive to replay old swatches. For how we make sure each swatch has exactly one weave, see logic puzzles you never have to guess, and for a different kind of grid logic try our Sown techniques guide.