## Teaser 2968: Gardening division

**From The Sunday Times, 11th August 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 numberCDE. In the middle, they have planted a square flowerbed of a length which is a single-digit numberFand area a two-digit numberGH.They have called in a gardener, who works for a single-digit

Ihours. He works for a whole number of minutes on the flowerbed and the remainder on the surrounding lawn. Each square metre of the flowerbed requiresN(a single digit) times the time spent on each square metre of the surrounding lawn. I have mentioned nine letters,A-Iinclusive, and each stands for a different positive digit.How many minutes does the gardener work on the lawn?

[teaser2968]

## Jim Randell 8:29 pm

on9 August 2019 Permalink |We can express the puzzle as a set of alphametic constraints and then use the general alphametic solver [[

`SubstitutedExpression()`

]] from theenigma.pylibrary to find the solution.The following run file executes in 140ms.

Solution:The gardener worked on the lawn for 99 minutes.The garden is a square of side 24m, giving a total area of 576m².

The flowerbed has sides of 9m, so has an area of 81m², leaving an area of 495m² of lawn.

The gardener works on the flowerbed for 81 minutes, at a rate of 1 minute per square metre of flowerbed. He then works on the lawn 5 times faster, at a rate of 1 minute per 5 square metres of lawn, so the 495m² of lawn takes 99 minutes. The total time is therefore 180 minutes, or 3 hours.

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