by Nick MacKinnon
The king’s square kingdom was subdivided into sixteen equal square subdivisions numbered 1 to 16 from left to right and from top to bottom.
He decided to share his kingdom with his daughters by dividing it into a number of pieces each consisting of one or more of the square subdivisions in a connected shape. Those he gave to his daughters were all of equal size, his being smaller.
After choosing subdivisions for himself and his eldest daughter, he noticed that in both cases the product of their numbers (or the number if only one) was a perfect square. He then found that there was only one way to suitably divide the remainder.
List the numbers of the subdivisions for the king and his eldest daughter.