The cow, I should stress, doesn’t belong to me – or even to Colin Wright, who told me about it. In honestly, I struggle to see any cows in it. All the same, I enjoyed the puzzle, and wanted to document it a bit without giving the answer away. However, there is always a risk that talking about how I solved it might give away the solution, so I’ll mark the point at which the discussion starts with a horizontal line as usual.

Here’s the puzzle:

Cut this shape into two pieces and reassemble them to make a square. Done it? Great. Now see if you can find another way.

Colin's Cow

Hopefully no spoilers below the line, but here comes the line in any event. All of the discussion pertains to the second, not-necessarily-obvious solution.

Talking of inadvertent spoilers, Colin says he spent two and a half years on this puzzle before someone gave what they thought was an information-free hint to show that they’d solved it, only for it to immediately suggest the solution to him and ruin the puzzle.

It didn’t take me so long, but neither did it jump out immediately, and I wanted to look at what I remember of my process.

1. Saying obvious things out loud

A previous me might look back with embarrassment at saying “I can turn it into a rectangle” aloud. That’s a variation on the first solution, and not especially difficult to find or useful. But that’s absolutely fine: quite often, I don’t know what’s useful until afterwards, and exploration is part of the process. Sometimes, an obvious thing leads to a not-obvious thing. It didn’t help here, but it wasn’t wrong to say it.

2. Drawing pictures

I’m starting to realise that I don’t typically see strong and vivid images in my brain. Luckily, I own a reMarkable ((Other drawing products, such as pencil-and-paper, are available)) and can draw reference pictures to look at. I drew several. I marked on the first solution. I marked on the rectangle non-solution. I drew a bigger one. I pointed at various corners. I drew on various lengths.

3. Thinking about what the answer looks like

I’m trying to make a square. How big must it be? Where can I get the right angles from? Must I use some existing right angles? Which ones might stay put? Which ones could I cut or move? How about edges?

4. Oo, that’s interesting, can I make it work?

I’m not going into detail on this for fear of spoilers; I’ll divulge that I came up with a hypothesis involving an edge and asked “if I wanted to put that edge there, where would I need to cut the rest of it to make it fit? And does it fit?”

5. Geogebra

Even after drawing it out and assuring myself it looked reasonable, I still wasn’t entirely convinced – so I mocked it up in Geogebra, interpolating the transformation between the cow and the square with a slider so I could see it move into place. It’s quite satisfying to see something like that actually work!

I enjoyed the puzzle, not least because I managed to get Colin to say he hated me ((He was joking. At least, I presume he was joking.)) and to get Dominika to curse Colin’s name ((Fairly sure she was joking, too.)). I don’t usually like dissection puzzles very much, but this one tickled me.

Still don’t see the cow, though.