Teaser 2759: King Lear II
14 August 2015
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From The Sunday Times, 9th August 2015 [link]
King Lear II had a square kingdom divided into 16 equal smaller squares. He kept one square and divided the rest equally among his daughters, giving each one an identically-shaped connected piece. If you knew whether Lear kept a corner square, an edge square or a middle square, then you could work out how many daughters he had.
The squares were numbered 1 to 16 in the usual way. The numbers of Cordelia’s squares added up to a perfect square. If you now knew that total you could work out the number of Lear’s square.
What number square did Lear keep for himself and what were the numbers of Cordelia’s squares?