# Sunday Times Teaser 3160 – Hymn Number Anagrams

*by Edmund Marshall*

#### Published Sunday April 16 2023 (link)

At Church on Sunday, the hymn board showed just four different hymn numbers, each having the same three, different, non-zero digits, but in a different order. I noticed that the first hymn number was a perfect square, and that there was at least one other perfect square, formed from the same three digits, which did not appear on the board. The sum of the four hymn numbers was a prime number. If I told you the first digit of that prime number, you would be able to tell me the first hymn number on the board.

What was the first hymn number on the board?

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There seems to be a flaw in this teaser since it has two solutions.

Are there really that many hymns?

Spot the not-so-deliberate mistake in my code. It leads to a unique solution, possibly the same as arrived at by the Teaser’s author.

Don’t be too hard on yourself John, as I also made the same error until

it was noticed by Frits.

I suspect you are right that the answer you found is that intended by

the teaser author but we won’t know for a while.

If you map to the square(s) on the hymn board rather than the four

hymns (and collect with a defaultdict(set) rather than a list) you

should see the two solutions.