The properties of dumbers too!

Welcome back to George vs the Listener Crossnumber, the quarterly report on things logical and numerical.

Apologies (particularly to setters) for the last few weeks of being whisper quiet. A big crash of busy stuff, an illness, and a very exciting writing project have taken up a lot of the time that I would usually spend solving and making terrible jokes about puzzles. And I know I should go back and write about the last few puzzles and my various ups and downs on them, but as you can see from the grids I’ve pasted – I actually solved them.

You don’t come to George vs the Listener for smugness and ability to solve at the drop of a hat.  There’s another blog chock full of that.  You come to George v Listener to hear of failure and misery.

Enter Piccadilly.  A setter of both letter and number puzzles, though I have only done one of the letter puzzles before.  This did look rather fun and definitely inventive – look what we have, a symmetrical grid, no two lights have the same starting square, and all of the instructions are statements about numbers that are also statements about their grid entries.

There is also a clear starting point – 1 has to be a cube and a square which means it is a power of six.  That limits it to 15625 or 46656, so 3 starts with a 6 and is a prime.  I marked the end of the prime answers with an x, knowing there had to be an odd digit in those positions, and then fiddled with the possibilities for 14 that narrowed it down to 118.  Working from there to get 2, 3 (and hence 6) was looking good, that set 12 and then 24 has to be 12+12 and oh shit there’s an even digit in a square marked with x.

My working grid for Listener 4464, The Properties of Numbers III by Piccadilly

I tried backtracking and got nowhere.  I don’t think there’s another starting point, surely.

The solution is out now and it seems I had overlooked another contender for 4 down (damn you online lists of squares!).

This was an impressive piece of setting by Piccadilly, and I am a little embarrassed to not be up to the task, but this is a massive victory to the Listener Crossword!

Game over, 4% completion.

Feel free to give me maths lecture after maths lecture, and see you next week when Yorick runs letters by us.

 

 

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