Mathematics, applications of mathematics to life in general, and my life as a mathematician.
Here is a famous matchstick puzzle based on the given picture.
Puzzle. Can you move three matchsticks to turn the fish around?
Here is my bonus puzzle.
Bonus Puzzle. Can you turn the fish by moving two matchsticks?
I figured out the answer to the bonus puzzle before puzzling out the original one. Then it took me a while to realize it was the answer to the bonus puzzle. Yes, you can turn the fish by moving two matchsticks.
I saw moving the 2 RightDown in to LeftUp relative to the central square for the bonus and then realized to solve the puzzle I could do a casework of sorts examining plausible locations for the central square in the implicit grid. At this point one realizes that there are already 5 matches located in the correct positions for say the square that is RightDown of the initial square.
When looking at the fish it is useful to see not a fish, but two letters F. This is how one finds the Bonus Puzzle has different solutions, depending on which matchsticks one decides to move.
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