## Latin Squares Puzzles

Latin Square puzzles were invented by Mark Thompson, and have appeared in Games Magazine. (Mark's description)

In a Latin Square puzzle, an N by N square is filled with N copies each of N different symbols. The symbols must be arranged so that each row contains exactly one of each symbol; ditto for the columns. The square is also divided into N outlined regions, and each region must contain exactly one of each symbol.

The puzzler is usually shown some of the symbols at the start; usually one of each symbol, one in each row, column, and region. Using these clues, and logic, the puzzler can uniquely place the remaining symbols.

The symbols are usually letters, but in the Rooftop Lights puzzle I used seven different colored lights instead. In addition to the usual hints, I also showed the contents of the regions as a string of lights. The puzzler has to determine which string belongs to which region, and in which order. To make this work, I chose a layout that had regions that didn't fork. This addition was made solely to make the puzzle easier for the less interested puzzler. The puzzle is still completely solvable without using the strings.

Most Latin Square puzzles I've seen were 6 by 6 or smaller. I've been working on a program to generate larger ones; thus the 7 by 7 one. It is a challenge to find layouts that (a) allow a Latin Square arrangement, (b) permit initial clues in the usual arrangement, (c) have a unique solution, and (d) have a reasonable solving difficulty. It was also challenging to find seven colors that were easily distinguishable to the eye.