Patches answers archive

October 2026 (19)

September 2026 (27)

Opening a past Patches board

Dates in the list link into the month page, which shows the full solution for each day of that month in order. Puzzle numbers are printed next to each date and rise by one per day: the window runs from #170 on 3 September 2026 to #207 on 10 October 2026. The only missing day is 5 September (#172), a board we don't hold.

The month page draws every rectangle in its clue's colour with each clue cell marked inside it, so you can check a board you solved, or rebuild one you missed, rectangle by rectangle.

Board sizes across the week

Twelve boards were 6×6, seventeen were 7×7 and eight were 8×8. Every Monday was 6×6, every Wednesday 7×7, and four of the five Saturdays and four of the five Sundays were 8×8. Tuesday leaned small (four 6×6, one 7×7) and Friday leaned medium (five 7×7, one 6×6).

That pattern makes the archive easy to sort by difficulty without opening every entry: the list's summary column shows each board's size, so a scan of the column tells you which days were the larger boards.

The number of rectangles followed the same weekly shape. Tuesday boards averaged 6.8 rectangles and Monday boards 7.8, while Saturday averaged 11.6 and Sunday 12.8, nearly twice Tuesday's figure.

Patches per board, by size

Each board is cut into as many rectangles as it has clues, one clue per rectangle. Bigger boards had more rectangles, but not much bigger ones: the average rectangle stayed around five cells on every size.

Strips outnumber blocks

Of the 361 rectangles, 211 were one cell wide: a single row or a single column. The rest were blocks at least two cells thick in both directions. Among four-cell rectangles the split was nearly even, 45 squares (2×2) against 43 strips (1×4). Among six-cell rectangles the block won clearly, 49 at 2×3 or 3×2 against 18 strips of 1×6.

The practical point: a large number is not a promise of a chunky shape. A 6 is more often a block than a strip, but more than one in four six-cell rectangles in the window was a single 1×6 line.

Area counts, smallest to largest

Small rectangles dominate. These are the number of rectangles of each area across the window:

Put another way, 298 of the 361 rectangles covered six cells or fewer. Only two rectangles in the whole window reached 16 cells, both on 7×7 Wednesday boards: #183 on 16 September and #197 on 30 September. A 16 on a 7×7 board can only be a 4×4 square or a 2×8 strip, and a 2×8 strip doesn't fit, so both had to be squares.

• 2 cells: 64
• 3 cells: 59
• 4 cells: 88
• 5 cells: 20
• 6 cells: 67
• 7 cells: 5
• 8 cells: 14
• 9 cells: 20
• 10 cells: 10
• 12 cells: 6
• 14 cells: 3
• 15 cells: 3
• 16 cells: 2

Prime areas leave no choice of shape

A rectangle of 2, 3, 5 or 7 cells can only be a strip, because those numbers have no factors other than 1 and themselves. In our window that covered 148 of the 361 rectangles, about two in five. Those clues are the cheapest place to start: the size fixes the shape, and only the direction and position are left to decide.

Fours, sixes and nines are where boards branch. A 4 can be a 2×2 or a 1×4, and as the counts above show, the boards used both almost equally, so a 4 never tells you which on its own. Look for an edge, a neighbouring clue or a shape symbol that rules one out.

Clues without a number

Not every clue carries a size. Of the 361 clues in the window, 127 had a shape symbol and no number, about 35 per cent. Nine boards numbered every clue, and two boards numbered none: #184 on 17 September and #193 on 26 September. An unnumbered clue still fixes the rectangle's proportions, and the rectangle's size comes from whatever space its neighbours leave.

Unnumbered clues were more common on larger boards: 8×8 boards averaged 4.4 of them, against 3.0 on 6×6 boards. Even so, the two boards with no numbers at all were a 6×6 and an 8×8, so a small board is no guarantee of numbered clues.

Shape symbols, counted

Most clues allowed any proportion: 208 of 361 carried the "any" symbol, against 74 tall, 47 wide and 32 square. The mix changed sharply between numbered and unnumbered clues. When a clue had a number, it was "any" 168 times out of 234. When it had no number, a specific shape was far more common: 44 tall, 23 square and 20 wide against 40 "any". In practice, a clue that withholds its size usually tells you its shape instead.

Shape symbols also mark the hardest clues to read at a glance. A tall clue with no number can be any rectangle taller than it is wide, so it often has to wait until the numbered rectangles around it have claimed their space.

Unusual boards worth studying

Each of these stretches a different skill.

None of these needs anything beyond the counting method; they just push one part of it further than a typical day does.

• #196, 29 September (7×7): only four rectangles, the smallest of them 10 cells. Big areas, few clues, lots of factor work.
• #205, 8 October (7×7): fourteen clues, every one marked tall, and ten of them unnumbered.
• #193, 26 September (8×8): eight clues and no numbers at all; six of the eight are squares.
• #184, 17 September (6×6): ten unnumbered clues on a small board, so sizes come entirely from the space left over.
• #186, 19 September (8×8): sixteen rectangles, the most on any board in the window.

Drilling the counting method

Our Patches guide recommends a counting method: total the known areas, subtract from the board, and see what the remaining space must hold. The archive is the place to check that drill afterwards, because each solved board is right there to compare with. When you open the live board, write down the factor pairs for every numbered clue before placing anything, then mark every prime clue as a strip and decide its direction. Mondays are the place to build the habit: every Monday board in the window was 6×6 with nine rectangles or fewer, so the whole exercise fits on one page of notes. Afterwards, open the day's entry here and check each rectangle against your notes.

When that feels routine, move to a board with several unnumbered clues and practise the reverse: work out the space each numbered rectangle claims, and let the unnumbered ones take the remainder.

Reset time and the newest entry

Patches resets at midnight Pacific time, and the new board joins the top of the list at that moment. Players well ahead of Pacific time, across Asia and Australia, meet each puzzle on the following calendar day, so searching by puzzle number is more reliable than searching by date from there.

The list always shows the newest board first, so once the reset has passed, the top row is the current day's puzzle and everything below it is history.

If a board doesn't match your memory

Check the number first, then the size. Because sizes follow the weekday closely, a 6×6 you remember from a weekend is probably a different day; no Saturday or Sunday board in the window was 6×6. If the number matches and the colours look different, that is just rendering: we draw each rectangle in its clue's colour, which may not match the shade on your screen exactly.

If something still looks wrong, compare the rectangles one by one with the clue cells. Every clue sits inside exactly one rectangle, and on every stored board the rectangles' areas add up to the full board: 36, 49 or 64 cells.