Roland Dürre
Wednesday April 12th, 2017

Another Logelei!

Since my last Logelei gave many people some joy (and brought others close to desperation), here is another one. However, it is
Basically very simple!

A house owner has a square-shaped patio paved with 64 simple square-shaped tiles (each measuring 30 cm x 30 cm). He wants to put 31 domino stones (he already bought them) over them. They are twice as big as the tiles, that is, their width is twice their length, i.e. 60 cm x 30 cm.

His special desire is that the two opposing corners should be left untouched by the domino stones. He wants cubic tiles with a very special symbol at those corners. He already bought the two of them (just as big as the original ones, i.e. 30 cm x 30 cm). Naturally, for aesthetic reasons, the domino stones cannot be halved.

He assigns the task to a craftsman. The craftsman is happy to do the job and starts his work. He leaves a corner open and starts positioning the domino stones.

Now here are the questions:
Will the craftsman manage to do it?

If yes, how?
or
If not, why not?0

I will publish the solution two weeks from now – and until then, I look forward to many  emails  suggesting a solution!

Here is some help: I, too, have a square-shaped patio 🙂

In 1968, Werner gave me this question while we were watching a boring soccer match in the Rosenau Stadium. He was five years my senior and already studied mathematics at TUM at the time. I was still a pupil at the Jakob-Fugger-Gymnasium. Unfortunately, I do not know the original source of this logelei, either.

RMD
(Translated by Evelyn)

1 Kommentar zu “Another Logelei!”

  1. Chris Wood (Sunday April 16th, 2017)

    Dear Roland, this one is too easy, especially for chess players. Do you know how to do a knight’s tour on an irregular board, (where that is possible)?

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