**From The Sunday Times, 15th November 2015** [link]

King Lear III had a square kingdom divided into sixteen equal-sized smaller square plots, numbered in the usual way. He decided to keep a realm for himself and share the rest into equal realms (larger than his) for his daughters, a “realm” being a collection of one or more connected plots. He chose a suitable realm for himself and one for his eldest daughter and he noticed that, in each case, multiplying together [the] plot numbers within the realm gave a perfect square. Then he found that there was only one way to divide the remainder of the kingdom into suitable realms.

What are the plot numbers of the eldest daughter’s realm and of the king’s realm.

The puzzle text on The Sunday Times website, uses “any” where I have placed “[the]”.

[teaser2773]

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I thought this was quite a good puzzle, involving several steps to arrive at the solution.

This Python program uses several useful routines from the

enigma.pylibrary. It runs in 135ms.Solution:The Eldest daughter gets plots 1, 2, 5, 9 and 10. The King keeps plot 16.The division of the kingdom is shown below:

There are three daughters, who each receive a realm of 5 plots. The King keeps a realm of 1 plot for himself.

The Eldest daughter’s realm is shaded red, the other two daughter’s realms are shaded blue. The King keeps the plot shaded black.