Make it a regular hexagon

Imagine pens that hold one animal each, and think about building them with 12 matchsticks. We tend to try making them as squares, but let’s shift that thinking. A triangular pen only needs three matchsticks, so… with a clever combination, you can form a regular hexagon. It’s a surprisingly tricky puzzle!

Move the two sticks at the bottom right to make the goldfish face upward.

When we see the phrase “change direction,” we tend to assume it means “turn 180 degrees”—right to left, up to down, and so on. If someone said “either up or down is fine” for this problem, it would click right away, wouldn’t it? Still, it’s kind of curious that with just this many matchsticks, the figure can look like a goldfish.

Move the rightmost matchstick to make “ONE.”

When you're told to “make a 1,” you’d naturally think you have to create the actual shape of the numeral “1,” right? But if you think about 1 in different ways—like “hitotsu,” “first,” “one”—your thoughts start to wander and then you go, “Aha!” That’s why it works. It’s a bit tricky for people who don’t know how to spell the English word ONE.

Move the two vertical matchsticks at the top to the left and right, and move the horizontal matchstick in the top center downward.

Since you only need to make three squares, it seems like there could be infinitely many answers, but if you want a neat arrangement with no surplus or shortage, there’s only one solution. Because there are no constraints regarding the leftover matchsticks, that might be the tricky part of this problem. Please try it with the mindset of “Let’s make exactly three squares with no more and no less!”

If you move the bottom matchstick of the 0 to below the space between the 1 and 0 and change its orientation, it becomes a “5.”

Because it’s half of ten, I can at least think to somehow make the shape of a “5,” but how should I move it? There’s no restriction saying “you mustn’t change the orientation,” so the shift in thinking to “let’s try changing the orientation!” is the key to solving the problem. Still, it’s a really well-crafted puzzle. I’d love to pose it to friends in my class who enjoy quizzes.