# Sunday Times Teaser 3056 – Rose Garden

*by Andrew Skidmore*

#### Published Sunday April 18 2021 (link)

The six rose bushes in my garden lie on a circle. When they were very small, I measured the six internal angles of the hexagon that the bushes form. These were three-digit whole numbers of degrees. In a list of them, of the ten digits from 0 to 9, only one digit is used more than once and only one digit is not used at all. Further examination of the list reveals that it contains a perfect power and two prime numbers.

In degrees, what were the smallest and largest angles?

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@Brian, line 19 upper limit is not always correct.

I didn’t check the line 20 upper limit

example: for sum_456 = 339 you don’t check combinations [112, 113, 114]

Thanks, it should have been (sum_456 – 3) // 3 + 1. I’ll correct it later.

Slow but steady. Thank you Brian, for the 3 angle 360° criterion

Credit for the alternate angle sum criterion goes to Jim Randell as I had forgotten about this constraint and initially got multiple solutions before being ‘rescued’ by Jim’s initial comment on this teaser.