The Magic of Logic (9)

Keeping kids happy and occupied in pandemic times

Time for another logic lesson? Recently I gave grandson Enders a new puzzle:

You have two hourglasses. One measures five minutes, and one seven minutes. You need to measure exactly thirteen minutes (to boil goose eggs perfectly?). How can you do this using these two hourglasses?

Enders and family spent quite a bit of time working on this, but could not find the solution. It is for some reason unexpectedly difficult.

In any case Enders struggled and then gave up. It was not an “okay-tell-me” resignation, but the “I’ll-work-on-it-later” kind. And a week or so after that I confronted him again. “No, I couldn’t do it,” he said grumpily. “Tell me what you have so far,” I said. He described his failed attempt.

“First I invert both glasses. When the five-minute glass runs out I invert it, and then when the seven-minute glass is finished… No, that is rubbish. It doesn’t work.” This is where I gave him the first and only hint. “No, keep thinking, Enders.”

We drew a picture in our minds: After seven minutes we have this situation. “Okay, I got it!” squealed Enders in delight.

And got it he had, perfectly. You, dear reader, can try to work out the continuation. It is quite easy, but for some unknown reason, difficult to complete in your mind. The solution is at the end of this article. Before peeking please try working it out yourself.

In the past month I gave this problem to a number of very smart kids — mostly full chess grandmasters, in their early teens. Most were unable to solve it. Just one reported that his mother, a microbiologist, had worked it out.

I also gave it to 14-year-old Leon, a remarkable young lad — a chess super-talent. Leon is from Goa, India, but has been stuck in Hungary and Serbia for a number of months, due to the pandemic. He was quite annoyed that he could not solve it quickly, but then took a resolute shower and had the answer.

“I really enjoyed the puzzle you gave me,” Leon wrote. “Please keep sending me more.” Another addict.

In the meantime son Tommy has come up with a new puzzle, which we suspect he might have invented:

You have three hourglasses, each runs for exactly one hour. You prepare one, lying on its side, to be able to measure half an hour. How can you do this?

This problem is seriously difficult, and I will not give a solution here (at least not yet). But in case you did not solve the thirteen-minute problem, the solution goes as follows: after the seven minutes have passed you have three minutes left in the five-minute glass. Turn over the seven-minute glass and let it run until the five-minute glass is finished (=10 minutes). Then turn the seven-minute glass over again and let the three minutes run back into the bottom. That will give you 7 + 3 + 3 =13. Bingo!

Previous logic articles in my Chronicles

Written by

Frederic Alois Friedel, born in 1945, science journalist, co-founder of ChessBase, studied Philosophy and Linguistics at the University of Hamburg and Oxford.

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