# Listener 4503

Joined: July 18th, 2017, 11:47 am
A most inventive take on the number properties style of puzzle that had a 'perfect' way in. Thanks Smudge.

Joined: July 30th, 2017, 9:35 am
I did enjoy this and found it quite challenging, but ...

The preamble states that "Each grid entry must be associated with exactly one of the properties". This is evidently false, because any number that is a fourth power (property d) is also a square (property a).

In the solution (and my uncertain submission) we also have, at 34a, 901: a clue number and entry that are both the sum of two different non-zero squares (property f) and numbers that are the reverse of primes, but not themselves prime (property m)

What was the intention of this statement?
Tony

Joined: July 16th, 2017, 2:19 pm
The preamble said that "Each grid entry must be associated with exactly one of the properties".

That isn't quite the same as saying "Each grid entry has exactly one of the properties".

According to my notes, 13a, 26a and 29a have to be associated with property f, therefore as the three entries associated with that property have been used up, 34a has to be associated with property m.

Joined: July 30th, 2017, 9:35 am
My own notes are, as always, scribbled and disorganised, but I don't deny the logic.

Saying what the clause isn't, however, whether correct or not, does not help to answer my question of what the clause is, of what its intention. How does that clause help the solving process? How does it constrain the solution?
Tony

Joined: July 16th, 2017, 5:07 am
The wording was both an accurate description of the allocation of numbers to properties and was useful to my solving. The list of square grid numbers includes 1 and 16, but they are also the only fourth powers (of which there are two examples) so can be excluded from the list of squares. All four remaining squares could then be ruled out of consideration for the other properties.

The false statement was in the penultimate sentence, and I didn't didn't discover the correction until long after completing the puzzle.

I found it one of the toughest numerical Listeners I've tackled, even though the maths was mainly straightforward. It took me most of the weekend to complete. Property f was a killer.