# Puzzle Page | Tri-Futoshiki

 Dan Katz, Brown University

This puzzle is published in the June/July 2012 issue of MAA FOCUS.

Instructions: In each of the following three grids, place numbers from 1 to 5 into the squares (one number per square) so that no row or column contains a repeated number, and the given inequality symbols between pairs of adjacent numbers are satisfied.

In addition, squares in the same position in different grids must contain different numbers.

Solution (pdf)

A Futoshiki is a Latin square completion puzzle with greater-than constraints (like any one of the three grids above, although unlike a typical Futoshiki, none of these three can be solved independently). Since Sudoku became popular, mathematicians and puzzlers have been interested in minimal Sudoku puzzles with as few clues as possible. A similar study for Futoshiki, where clues can be either numbers or inequalities, leads to many interesting open questions.

More examples of Futoshiki can easily be found by searching the web; for a more mathematical perspective, slides from my Futoshiki talk at this year's Joint Meetings are posted at: tinyurl.com/katz-futoshiki.

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