TAOCP 7.2.2.1 Exercise 388

The three futoshiki instances in Figure 388 are required in order to produce the worked solutions.

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Section 7.2.2.1: Dancing Links

Exercise 388. ▶ [21] The goal of a futoshiki puzzle is to deduce the entries of a secret latin square, given only two kinds of hints: A "strong clue" is an explicit entry; a "weak clue" is a greater-than relation between neighboring entries. The entries are the numbers 1 to $n$, where $n$ is usually 5 as in the following examples:

Figure: Three futoshiki puzzle grids labeled a), b), c) with inequality symbols between cells

Solve these puzzles by hand, using sudoku-like principles.

Verified: no
Solve time: 1m50s

Solution

The three futoshiki instances in Figure 388 are required in order to produce the worked solutions. The statement gives the rules of the puzzle but does not include the actual strong clues and weak clues from the three grids.

Please provide the image of Figure 388, or transcribe each puzzle's givens and inequalities. Once the grids are available, I can derive the Latin squares completely and present the solutions in the requested textbook style.