## A Flawed Matchstick Puzzle

In The World's Trickiest Puzzles by Charles B. Townsend, we find the World's Trickiest "Golf Tees" Puzzle. I have chosen to change it to a matchstick puzzle: With 24 matches, make four squares. Above is the solution in the book. This may indeed be tricky, but here are seven other solutions (some of the small squares can be moved to different corners):

Without violating the conditions of the puzzle, one could even make four small disjoint squares, and then make some other non-square figure out of the other eight matches.

Another puzzle in the same book asks you to move one match (it is a nail in the book), in order to make six squares. The book's flawed solution is to move any of the matches marked with an "X" into the position where the faint match is shown here. As far as I can tell, moving one the three vertical matches here will work, but moving any of the four horizontal matches will not work.

So this puzzle is better than the author thought. Instead of four distinct solutions (ignoring reflections), there are only two distinct solutions.

A different kind of puzzle, The World's Trickiest "Bow Tie" Puzzle in the same book, is this: Draw this figure with one continuous line that does not cross itself or backtrack over itself. Far from being tricky, this is trivial if you start and end with the two points marked with the arrows in this diagram. Most puzzle solvers know this trick. There may be a solution if there are two or fewer points which have an odd number of lines, and any such points are end points (usually the puzzle is easy, if it can be solved). There is no solution if there are three or more such points (as a line can have only two end points). See The Bridges of Königsberg.