Fun with Maths and Physics

Ya. I. Perelman

By the Way

Scissors and Paper

Three pieces from one cut* Placing a strip on an edge* Charmed rings 0 Unexpected results of cutting 40 Paper chain 0 Thread yourself through a sheet of paper.

Perhaps you think, as I once did, that there are some unnecessary things in this world. You're quite mistaken: there is no junk that might not be of help sometime for some purpose. What is useless for one purpose, comes in handy for another, and what is useless for business might be suitable for leisure.

In the comer of a room being repaired I once came across several used postcards and a heap of narrow paper strips that had been trimmed from wall paper. "Rubbish for the fire," I thought. But it turned out that even with this junk one can interestingly amuse oneself My elder brother Alex showed me some things you could do with them.

He started with the paper strips. Giving me a piece of strip about 30. centimetres long, he said: "Take a pair of scissors and cut the strip in three..."

I was about to cut but Alex stopped me: "Wait a bit, I haven't finished yet. Cut it into three with one cut of the scissors."

This was more difficult. I tried one way and then another, and then began to think my brother had posed a virtually impossible problem. Eventually it occurred to me that it was absolutely intractable.

"You're pulling my leg," I said, "It's impossible."
"Well, think again, maybe you'll work it out."
"I have worked it out that the problem has no solution."
"Too bad. Let me."
Brother took the strip, folded it in two and cut it in the middle to produce three pieces.

"You see?"
"Yes, but you've folded the strip."
"Why didn't you?"
"You didn't say I could."

But I didn't say you couldn't either. Simply agree that you didn't see the solution."
"All right. Give me another problem. You won't catch me out again."

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