Step 5 of 5

Mind the leftovers

A placement isn’t right because it fits. It’s right because of what it leaves behind.

The rule of thumb: Every cell needs a patch: a placement that strands a gap no clue can fill is wrong.

Every cell has to end up in some patch. So when a clue has two ways to go and both fit its badge and number, don’t toss a coin: try each one in your head and look at the empty cells it leaves around it. If a gap is out of reach of every remaining clue — boxed in by patches, edges and other clues — nothing can ever fill it, and that placement is wrong, however neat it looked.

These practice boards each reach a moment, a couple of patches in, where a clue still has more than one way to go — and every way but the right one cuts off some cell that another clue could have reached, leaving it stranded exactly like that. The worked example above shows the first of those wrong ways.

Where to look: Any moment you’re choosing between two placements. Check the awkward cells near the edges of each option, not the placement itself.

Worked example

A real position from a board built around Mind the leftovers. Purple: what the reasoning rests on. Dashed: the patch in question. Green: what it proves.

The clue at row 1, column 2 — 3, wide rectangle — has 2 ways left. This one (hatched) fits its badge and number. But look at row 6, column 1 (purple): with this patch down, no remaining clue can reach it — not even the clue at row 4, column 1, which could before. It would be stranded.

So the patch goes the one way that strands nothing — and row 6, column 1 stays within reach of the clue at row 4, column 1, which covers it in the end. The leftovers decided it.

Practice it ↓