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Difficult Legacy - Puzzle of the Week


A square lot with four trees is divided among four heirs. The four surfaces should have the same shape - and each contain a tree. Is that possible?

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The legacy is huge.

It is a square field where different types of grain are grown.

In addition, there are four large walnut trees in the field.

The parents want to share the property as fairly as possible among their four children.

The two daughters and the two sons should have fields of the same size and shape1.

In addition, there should be a tree on each of the four new properties.

How do the parents have to divide the square field?

1 It should be possible to convert the four new plots into one another by rotating or shifting - or by a combination of rotating and shifting.

The following figure shows a division of the square that meets the requirements of the task.

It is a swastika variant, whereby the arms of the cross are significantly longer and are not only bent once, but three times.

Apart from a mirroring of this division, I am not aware of any other solution.

If you have discovered another variant, I would be happy to receive a short email.


I discovered this puzzle in the book "New Mathematical Riddles" by Michael Holt.

If you missed a puzzle from the past few weeks, here are the most recent episodes:

  • How big is the circular ring?

  • Buying a bicycle with counterfeit money

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  • How far is it to the neighboring village?

  • How old is sophie

  • Triangle searched on three circles

  • Pirates fight over 120 gold coins

  • December 31st wins

  • What time is it?

  • Pretty weird

Source: spiegel

All business articles on 2021-10-24

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