I found a puzzle on reddit that immediately grabbed me: toggle one pixel in this picture to make it correct.

71 puzzle

I’m not going to spoil it here. Play with it if you want to. Click the link if you want to see the solution. The question I want to look into is, why is this such a lovely puzzle? There are many reasons. Here are some of mine.

Tidy presentation

It looks sleek, doesn’t it? More legible than matchsticks or digital clocks, a bit of a public transport feel to it – even the colours are warm and inviting.

There’s a neat almost-symmetry to it, as well – all those 71s and 1s arranged together.

Familiar but different

I mentioned the matchsticks and digital clocks, and I feel like this puzzle belongs in the same family. It’s not just a friendly picture, it’s a friendly puzzle type.

However, it’s significantly different: moving a match or toggling a segment on a clock is a dramatic change; toggling a single pixel is barely a change at all!

It’s also mathematically familiar. Here we go, it’s the difference of two squares, so it’s $71^2 - 1$… only that’s way too many pixels.

Appears impossible

The pixel restriction makes it feel impossible. What can you do with one pixel? You could (and some people tried to) argue that a dot inside or after the = makes it look like a $\neq$ or a >, but that’s a serious stretch. You can’t add a digit. It’s the kind of thing that jumps out at you.

@graf_paper put it well:

Ha, I tried so many things, including scepticism, disbelief, decimals, multiplication, and trying to change a digit with one pixel. So many things until I realized the answer!

Obvious in retrospect

Once you’ve got the answer, it’s completely obvious and completely lovely and you’re almost compelled to share it with everyone.

Some depth

Like many good puzzles, there’s a bit of ongoing depth to it: there’s a natural extension. Being deliberately vague so as to avoid spoilers, one might ask “does it work for any others?” and “does it work for still others if we change something?”

There are likely other good questions to ask – and there are likely other good reasons to love the puzzle. If you have others, I’d love to hear them!