Five Squares Into Four Challenge

The Challenge

The challenge is to move two sides (simulated matchsticks) and change the configuration of five squares into a configuration of four squares. The sides may not be removed. They all remain in play. They all stay the original size. There are no tricks to the solution like laying one side on top of another.

The mechanics of making moves are to select a side to move by tapping on it and then selecting an unoccupied place on the grid to move it to. When a side and an unoccupied place are both selected, the side will move. Dragging does not work. The player may also select the unoccupied place first and then select the side to move. When a side is selected, by tapping on it, it will change color and there will be a "tock" sound. If an unoccupied place is selected first it will turn blue and there will be a "tick" sound. If you change your mind before selecting both a side and an unoccupied grid place, just select something else and the selection will change.

A Hint

How many sides (matchsticks) are there? 16? Right! Are 16 enough to make four squares? In the starting configuration there 16 sides that make five squares. To form more than four squares some sides must be shared by adjacent squares and those sides are the sides of more than one square.

Background

I became acquainted with the Five Squares Into Four puzzle in the early 1980's but I suspect that it is much older. It was a popular bar bet and usually done with real matchsticks, the old wooden ones. A rumor at the time was that the puzzle was presented to a graduating class at West Point of several hundred cadets in an auditorium with viewgraph projector technology. All graduating cadets receive a Bachelor of Science degree. At the end of 20 minutes about half of the class had solved the puzzle of Five Squares Into Four. At the end of an hour, 15 cadets were still struggling. Apparently, there was no relationship between class standings and success at solving the puzzle. What I have found interesting in my own experience is that a few women have solved immediately, in about 20 seconds or less. I do not recall a man solving in less than five minutes.

While the challenge is to change the configuration from five squares to four squares by moving only two sides, this provision is not strictly enforced. A player can make as many moves as they wish. After each move the program checks for a solution and responds appropriately. After getting a solution, a player can continue to move the sides around and whenever the configuration has exactly four squares, it will be reported. Alternately, after solving, or at any time, a player can hit the reset button in the lower right of the grid and the configuration will be reset to the starting configuration and the timer reset.

If you give up, you can select the "play" button in the lower right corner of the main view and you will be shown the solution. After the solution configuration is displayed about 10 seconds, it will change to the starting pattern.

The Solution Configuration Looks Like This:

The solution configuration blinks on and off for about four seconds.

Use the following link to get a 5:10 minutes video on YouTube. FiveSquaresIntoFour