Sunday Times Teaser 2773 – King Lear III
by Nick MacKinnon
Published: 15 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 any 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.
List the plot numbers of the eldest daughter’s realm and of the king’s realm.