The tetrahedron puzzle

大家都知道甚麼叫正四面體吧？

將一個正四面體切成兩半，交由別人重新拼合成正四面體，有幾難？

研究人工神經網絡的著名學者 Prof. Geoffrey Hinton 說，原來這是很難的，許多麻省理工的教授都搞唔掂！以下是其演講 "What's wrong with convolutional nets?"（連結）的一部份 transcript（從 13:50 開始），相當惹笑。

Here's something you wouldn't believe. I take a simple object, like a tetrahedron. A tetrahedron is a pyramid with a triangular base. And I slice it with a plane. That's a flat thing ... I slice it with a plane. Uhm, so I get two pieces. And then I take an intelligent person, and I give him the two pieces, and I say "OK, make a tetrahedron." And I make sure he knows what a tetrahedron is. And he can't do it. Now I clearly ... now you don't believe that, presumably. It's just two pieces. Surely you can put it together to make a tetrahedron.

I present the experiment today to MIT professors. I got one sample thirty years ago, that's a professor called Carl Hewitt. He is very smart. I gave him the two pieces and ... he looked at them for a long time ... he didn't really play with them but looked at them for a long time, and determined whether he could write down a proof whether it's impossible. [laughter] So, his time to solve the puzzle is infinite. [laughter] OK?

Today I've been doing the experiment to MIT professors, and the number of minutes they take to solve the problem is about the number of years they've been in MIT. [laughter] Roughly speaking, it's definitely very ... the length of time is very positively correlated to how long they have been in MIT. [laughter]

So now I'm going to show you this puzzle, because it's extraodinary. It can't be so hard. It's completely trivial, and there's an obvious way to solve it that people don't figure out. They figure out in a few minutes, but, OK, here's the two pieces ...

（之後 Prof. Hinton 用了幾分鐘示範一些人解這個謎題時是多麼困難）

Why is this puzzle almost impossible? Why is it so hard? 'Cos it's a two-piece jigsaw puzzle. [laughter]

And the MIT professors, and ... oh, incidentally, I tried this on a Google vice president, just to reassure the MIT professors. I gave these two pieces to the Google vice president and said, "This is really a hard task. Can you make a tetrahedron?"

欲知 Google 的 VP 同 MIT professors 相比，結果如何，請看演講片段。