Futoshiki

All the usual strategies for "Latin square puzzles," (Sudoku, KenKen, Cartouche) apply to Futoshiki puzzles as well.

Strategy:

If a board has size n, and there is a chain of inequalities, \(x_1 \lt x_2 \lt \ldots \lt x_k,\) then the first cell in the chain cannot be greater than \(n - (k - 1),\) and the last cell cannot be less than \(k.\) For example, on a \(4 \times 4\) board, with a chain \(a \lt b \lt c,\) we can deduce \(a \le 2,\) and \(c \ge 3.\)

As a special case, if we have \(a \lt b,\) in an \(n \times n\) grid, then \(a \le n - 1,\) and \(b \ge 2.\)