GridWits

Arrangement Check

Hard Used by Smart Hint

A combination has to fit the cells, not just the total: if every combination containing this digit leaves some other cell in the run with nothing it can take, the digit is impossible here.

3 3 10 3 4 5 6 7 1 2 1 2

How it works

  1. Three cells sum to 10: the combinations are 1+2+7, 1+3+6, 1+4+5 and 2+3+5.
  2. Each right-hand cell is capped at {1, 2} by its own 3-in-two down run, so between them they can only ever supply a 1 and a 2.
  3. Adding up isn't enough — the combination has to be dealt out one digit per cell. 1+3+6, 1+4+5 and 2+3+5 each leave a digit with no cell that accepts it once the left cell takes its share.
  4. Only 1+2+7 can be arranged, so the left cell is 7.