Square out of a Plus
I once saw a TikTok video featuring a puzzle: four matches were arranged to form a plus sign, and the challenge was to move one match to create a square. The solution shown differed from what first came to my mind, so I decided to share the puzzle with my students. Instead of drawing a diagram, I described it to them in words.
Puzzle. Arrange four matches to form a plus sign. Move one match to form a square.
Most of my students gave the same solution shown in the video: moving one match slightly away from the center to create a square in the center, with the inner edges of the matches forming its borders. Not all the students were as lazy as I was; some drew pictures to illustrate. One example is shown below, where the resulting square is in green.
My solution, also discovered by a couple of students, was to move one match to form the number 4, which is a square.
I am glad I didn’t provide a picture because it led to two unexpected solutions. For the first one, imagine a 3D shape out of four matches where one projection forms three sides of a square, and the other one is a plus sign. We can take the match from the plus sign that is not a side of a square and use it to complete the square. The second solution is shown below. The arrangement already contains a small square, so you can take a match and put it back. Being lazy brings benefits!
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Ivan:
In the first picture there are 2 squares: the green one and the unseen one (the one whose diagonals are formed by the matches). So, a rewording of the puzzle will make it harder to solve.
13 November 2024, 8:17 pm