Teaser 2773: King Lear III
15 November 2015
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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]”.