# 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 $$b \ge 2.$$