Technique 5 of 5 · Expert boards
What-if
When nothing else works, test a cell. Suppose it holds a crown, follow the simple steps from there, and see whether some row, column or color runs out of cells. If one does, that cell can't hold a crown.
The idea
This is not guessing. You don't keep the test crown and hope for the best. You follow only forced steps, and if they lead to a dead end, you have proved something: the cell you tested is wrong. Cross it out, take the test crowns back, and carry on with the board as it was.
The example
This 9×9 board is stuck for the four simpler techniques. Try a crown at row 1, column 1, in the red region. It forces a chain of last cells:
- yellow must go to row 2, column 7,
- then orange to row 3, column 5,
- then teal to row 6, column 4,
- then green to row 5, column 9.
At that point the blue region has no open cell left. A crown at row 1, column 1 leads to a dead end, so it can't be right. Cross it out, undo the test crowns, and look again: the board is one cell smaller, which is often all a simpler technique needs.
How to spot it
- Test cells that see a lot. A cell next to several open cells, or in a crowded row, fails fastest.
- Keep the test short. Inside the test, use only Last Cell and the easy steps. If you find yourself needing to guess inside the test, abandon it and pick another cell.
- Mark your test lightly. On paper, use a dot instead of a crown so it's easy to erase. In Logic Legends, Hint runs the test for you and tells you which cell fails and which color runs out.
Why it works
If a crown at a cell forces, by rules you can't break, a situation the rules forbid, then that crown can't be part of the one true answer. It is the same reasoning as a proof by contradiction.
In Logic Legends
The hint calls this step What-if and names the cell it tested and the color that ran out. Only Expert boards need it; every other board can be solved with the first four techniques.