# an esoteric matchbox

Seeing a vast repository of matchstick puzzles, Professor Moriarty determined to create one of his own. Behold, his greatest crime yet, the best and worst matches puzzle to ever grace this earth with its presence. Move as few matches as you can to make another equation that is still true. (Turning the = into ≠ is frowned upon.)

By the way, this is read as this (or if you want to be like @Someone, it can be read as something else): $$\int x \, dx = \frac{x^2}2 +C$$

Note: If you wish to move more than the minimum matchsticks, or do something cool/interesting, that may be acceptable as well.

If you want the link to the primitive Google Slideshow I used to create the graphic, you can make a copy of the slideshow and manipulate the puzzle much more easily, either for your own answer or just to mess with it in a more concrete way. The slideshow is here.

• It looks as though I don't have to move any matches (or if I have to move one I can move it just slightly) and the equation is true. Is there something I'm missing? Nov 1, 2023 at 16:23
• Yes, sorry. I have made an edit. The goal is to create a new equation that is still true, by moving as few matchsticks as possible. Nov 1, 2023 at 16:24
• The integral looks like an eighth note…is it possible to use that? Nov 1, 2023 at 16:54
• @Someone Lol, sure Nov 1, 2023 at 17:01
• Please don't close this puzzle. I like it :) Nov 3, 2023 at 6:21

## 3 Answers

Using the same equation (as other answers), by moving

One match from + and add to C.
$$\int x \, dx = \frac{x^2}2 - t$$

Second attempt: I have moved

3 matchsticks

$$\int x^6 \, dx = \frac{x^7}{7} - C$$

First attempt: I have moved

8 matchsticks

$$\int \frac{1}{x} \, dx = \ln |x| +C$$

• you can also move the top of the C to make it +L, just one match. Or make it +Z. Nov 3, 2023 at 11:10
• I like your 3-matches $x^7$ solution. The 1-match $+t$ solution just begs the question "what is variable $t$?". The original $+C$ equation is self-explanatory because the integral is indefinite and it's a well-known convention that $C$ means "any constant", but there is no such convention for $t$.
– Stef
Nov 3, 2023 at 12:12
• @Stef I could have changed it to F but that has a function. I only posted that 1-match solution because apparently, minor changes to the original equation are acceptable :) Nov 3, 2023 at 12:41

How about only moving

1 matchstick?

It's kind of a trivial solution, but:

or, $$\int x \, dx = \frac{1x^2}2 -C$$

• Is that "another equation"? Nov 1, 2023 at 22:16
• I think that's up for op to decide, but I would argue it's equivalent but distinct. I do like both of your solutions tho Nov 2, 2023 at 0:16
• It's creative, and appears different, it counts! Nov 2, 2023 at 12:46

How about this?

2 matchsticks - I removed one matchstick to get a minus, and rotated another one to get an equals sign. If you want, the removed matchstick can be placed anywhere to double a line.

$$\int x \, dx - \frac{x^2}2 = C$$