by Danny Roth
Published August 11 2019 (link)
George and Martha’s garden is a perfect square of length (whole number of metres) a two-digit number ab. The area is a three-digit number cde. In the middle, they have planted a square flowerbed of a length which is a single-digit number f and area a two-digit number gh.
They have called in a gardener, who works for a single-digit i hours. He works for a whole number of minutes on the flowerbed and the remainder on the surrounding lawn. Each square metre of the flowerbed requires n (a single digit) times the time spent on each square metre of the surrounding lawn. I have mentioned nine letters, a-i inclusive, and each stands for a different positive digit.
How many minutes does the gardener work on the lawn?