Contradiction
Extreme
Used by Smart Hint
Placing this height in this cell forces some row or column to have no valid arrangement left — so that height can be ruled out here.
- Cells that establish the pattern
- Where the conclusion lands
- Height ruled out
How it works
- The last resort, shown on a case small enough to check by eye. The clue says two buildings are visible along this row.
- Suppose the first cell were the 4. Nothing behind the tallest building can be seen, so exactly one building would show — and the clue wants two.
- The supposition breaks the board, so it was wrong: strike the 4.
- That is the whole method. Place a height, propagate every constructive technique forward on a scratch copy, and if the position becomes impossible — a cell with no candidates left, or a clued line with no legal filling — rule that height out.
- In a real solve you'd never need it here (Visible-Count Bound catches this exact case in one step). It earns its keep on positions where every constructive rung has already run dry, and it only ever looks as far ahead as a person could trace by hand.