The how to play Sown page lists the five ideas in order. Here we go further, on 9x9 Hard and 10x10 twin gardens. Squares are named row first, then column, counting from the top left, and to dot a square means to mark it empty.
What the level tells you
A garden's level comes from the hardest idea our solver needed, which is useful when you are stuck. An Easy 7x7 garden needs nothing beyond a plot squeezed into one line, and uses that idea at least twice. A Medium 8x8 garden needs the starving idea (a square whose seed would leave a row, column or plot with no room) at least twice, and nothing harder. A Hard 9x9 garden is only published if it needs a group of plots at least once. Sunday's twin garden is capped on total effort rather than on one idea, and no daily garden at any level ever needs a trial-and-error "what if".
So on a stuck Medium, a starving square is waiting somewhere; on a Hard, look for a group. Also, daily plots always have at least two squares (three from 8x8 up), so there are no free one-square plots.
Small plots kill more squares than you think
A square can never hold a seed if that seed would dot every free square of some plot. A seed dots in two ways: by touching, and by filling its own row and column. Most missed deductions come from checking only the touching.
A two-square plot
Say a plot is just row 5, columns 3 and 4, side by side. The squares directly above the pair (row 4, columns 3 and 4) each touch both halves, so a seed in either would leave the plot empty. The same goes for row 6, columns 3 and 4. Those four squares are dead. The diagonal squares at the ends only touch one half, so they survive.
A three-square corner
Now take an L of three squares: row 5 column 3, row 5 column 4 and row 6 column 3. The inside corner, row 6 column 4, touches all three, so it is dead. Less obvious: row 4 column 3 touches the top two and shares column 3 with the bottom one, so it is dead too. By the same reasoning row 5 column 2 goes (it touches two and shares row 5 with the third). But row 4 column 4 touches only the top two and shares neither a row nor a column with row 6 column 3, so it stays open.
Plots and lines that own each other
The squeezed plot works both ways round: a plot inside one row owns that row's seed, and a row inside one plot owns that plot's seed. Recheck both directions whenever a few dots go in.
Two plots confined to two rows
Groups are the same idea scaled up. If two plots between them only have free squares in rows 6 and 7, then those two plots need two seeds and must take them from rows 6 and 7. Rows 6 and 7 only have two seeds to give. So both of those rows' seeds are spoken for, and every other free square in rows 6 and 7 can be dotted. Neither plot has to fit in one row. Our solver looks for groups of up to three plots in three lines, and the reverse: two columns inside two plots, which clears the rest of those plots.
How to spot a group without testing everything
- Look for plots whose free squares span exactly two rows or two columns, then ask whether another plot lives inside the same two lines.
- Check pairs of edge columns and edge rows, which often sit inside two plots.
- A group only helps if it clears something, so skip pairs of lines with no other free squares.
Worked example: Sown No. 12
Sown No. 12 (a Hard 9x9 from Saturday 31 October) tours these ideas. Open the Sown No. 12 answer page to follow along.
- The slate plot is three squares in a line: row 9, columns 5 to 7. Its seed must be row 9's seed, so dot the rest of row 9.
- That leaves the sand plot (row 8 column 1, and row 9 columns 1 to 3) with one free square, row 8 column 1. Sow it. That clears row 8 and, among others, row 7 columns 1 and 2.
- Teal has lost its squares in rows 8 and 9, leaving only row 6 column 7 and row 7 column 7. Teal is squeezed into column 7: dot the rest of that column.
- A seed at row 6 column 5 would touch every free square left in the pink plot (row 6 columns 4 and 6, row 7 columns 4 to 6), so it is dead. Column 7 now has just two free squares, so any square touching both is dead too: row 6 column 6, row 6 column 8, row 7 column 6 and row 7 column 8.
- A seed at row 7 column 3 would wipe out pink as well (it touches row 6 column 4 and shares row 7 with the rest), so that goes. Pink is down to row 6 column 4 and row 7 columns 4 and 5, and teal is down to its two squares in column 7.
- Here is the group. Pink and teal now live entirely inside rows 6 and 7, so those two rows give their seeds to pink and teal. Dot the other free squares of rows 6 and 7: row 6 columns 2, 3 and 9, and row 7 column 9.
The rest follows the same pattern: more starving squares, two more groups (one is columns 8 and 9 inside the sunflower and sky plots), then a cascade of last free squares.
Twin day: thinking in pairs
On Sundays every row, column and plot needs two seeds. Everything above still applies, with a twist: a plot can run out of room while it still has two free squares, if they touch.
Room for two
In Sown No. 13 (Sunday 1 November) the lavender plot is five squares: row 2 columns 7 to 10, plus row 3 column 10. The last three of those all touch each other, so they hold one seed at most, and lavender's other seed must be at row 2 column 7 or 8. Any square that would dot both of those is dead: row 1 columns 7 and 8, and row 3 columns 7 and 8. Row 3 column 9 goes too, because it touches everything except row 2 column 7, leaving room for one seed, not two.
Three in a line needing two
The sky plot in the same garden is row 3 column 9 plus row 4 columns 8 to 10. Once row 3 column 9 is dotted, sky is three squares in a line needing two seeds that do not touch: the two ends, row 4 columns 8 and 10, which are also row 4's two seeds. Whenever a plot or line needs two seeds from a run of three, sow the ends.
Boxes: one empty in every pair of rows
Take any two neighbouring rows and split them into five 2x2 boxes (columns 1 and 2, 3 and 4, and so on). Two seeds in one box would touch, so each box holds one seed at most. The two rows need four seeds between them, so exactly four of the five boxes get a seed and exactly one stays empty. The same is true of any two neighbouring columns. As soon as one box in a pair of rows is fully dotted, every other box in that pair must get exactly one seed, and a box with a single free square left gets its seed straight away. So a seed that would empty a second box in the same pair of rows is impossible.
Quick checklist
- After every seed, make sure all eight neighbours and the rest of its row, column and plot are dotted.
- Around every small plot, test the squares touching it for row and column clashes as well as touching.
- After every few dots, check each plot against the rows and columns it now covers, and the other way round.
- Stuck on a Hard? Look for two plots sharing two lines, or two edge columns sitting inside two plots.
- On twin day, look for touching squares that can only hold one seed, runs of three that need two, and pairs of rows with an empty box.
Try the ideas on today's Sown, or replay gardens from the Sown answers archive. For how we make sure every garden has one solution, read logic puzzles you never have to guess.