## Some Matchstick Puzzles

Geometric puzzles:

 Puzzle #1: Here are six matchsticks arranged to form one equilateral triangle. Can you rearrange the six matchsticks to form four equilateral triangles? The solution is at the bottom of this page. Puzzle #2: Here we have an olive (looking strangely like a dime) in a martini glass. Move two matches, to redraw the martini glass so the olive is outside the glass. Puzzle #3: This one is a little tricky. Move one matchstick to produce a square. Puzzle #4: Start with this grid of 12 matchsticks, remove two of them so that there are only two squares left. Puzzle #5: Move three matchsticks, and make the fish turn around and swim the other direction. Puzzle #6: Move two matchsticks to make only four identical squares. Puzzle #7: Move three matchsticks to make three identical squares (and nothing else).

Jokes and riddles:

 Puzzle #1: Move two matchsticks to change three into six (without cutting or breaking matchsticks). Puzzle #2: With matchsticks, show that seven is half of twelve. Puzzle #3: To these six matchsticks, add five more, to make nine.

A puzzle from Puzzle Playground (puzzles.com):

Insert the four matches into the square, in order to dissect the square into two identical pieces.Puzzle Playground gives one solution. But there are others.

Solutions

Geometric Solutions:

 Solution #1: The traditional solution is to form a regular tetrahedron (see Regular Solids), an example of lateral thinking, as it requires using the third dimension. Dr. Matrix's readers provided numerous alternative solutions using only two dimensions, as we did not forbid the overlapping of matches or triangles. This Star of David, with eight triangles (six small and two large ones), would seem to be the best solution.Another restriction (besides disallowing overlapping) which would force the tetrahedron is that all of the triangles must be the same size. Solution #2: Here is the solution, moving the horizontal matchstick, and the one on the far right. Of course you remove the olive by turning the glass upside down. Solution #3: We make a small square between the four matchstick ends, as shown. Solution #4: Here is the solution. This would have been even simpler, if I had mentioned that the starting diagram showed five squares. Solution #5: Move the faint matches in this diagram. Solution #6: Only two matchsticks were moved. Solution #7: Only three matchsticks were moved.

Jokes and riddles, solutions:

 Solution #1: We move the left two matchsticks, to make a Roman numeral VI. Solution #2: The solution to this is to make twelve in Roman numerals, as shown. The top half is VII, or seven. Just remove the bottom half. Solution #3: We spell out NINE, as shown.

A puzzle from Puzzle Playground (puzzles.com), solutions:

Above left is the solution shown at Puzzle Playground. But there are others, involving changes in the angles.