# Sunday Times Teaser 3124 – Lawn Order

*by Colin Vout*

#### Published Sunday August 07 2022 (link)

A gardener was laying out the border of a new lawn; he had placed a set of straight lawn edging strips, of lengths 16, 8, 7, 7, 7, 5, 4, 4, 4 & 4 feet, which joined at right angles to form a simple circuit. His neighbour called over the fence, “Nice day for a bit of garden work, eh? Is that really the shape you’ve decided on? If you took that one joined to its two neighbours, and turned them together through 180°, you could have a different shape. Same with that one over there, or this one over here — oh, look, or that other one.” The gardener wished that one of his neighbours would turn through 180°.

What is the area of the planned lawn, in square feet?

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This new version replaces my initial very slow and incomplete solution. It is now a full solution based on the approach that Frits uses in his version published on Jim Randell’s S2T2 site here. It now runs in about 1 second compared with over 2 minutes in my first version.

@Brian,

Do you allow a rotation to form the same circuit?

Only one solution passes my own rotation check (based on forming a different non-crossing closed circuit).

Hi Frits,

The strip of length 16 is always placed first along the x-axis and y values

below the x-axis are not allowed. So rotations of complete circuits won’t

occur. It finds the eight different shapes that gardens can have (slowly!).

Brian

partial solution: doesn’t calculate area