Crossword Help Forum
Forum Rules

The clues...

Clues should be in the form of hints.

The theme....

Help with the theme should be just a nudge, a pointer in the right direction - and definitely not anything that would spoil the puzzle for others. Any posts which, even inadvertently, reveal too much of the theme will be removed.

There are many regulars on the Listener threads, but newcomers are always welcome.
The Listener is a unique puzzle and should be treated with respect.

I was able to solve this by implementing an algorithm in computer code. I believe there are 144 ways to fill the grid excluding the four unclued entries...and then it's a matter of finding the unique combo that allows you to determine the 6-digit entries.

By the way, there are 313 pairs of 6-digit numbers (a,b) such that b is a multiple of a and also an anagram of a...

I can't imagine solving this without computer help

Well done on solving it, but clearly that’s not the intention behind the puzzle, which should be solvable with a pencil, paper and calculator, which is what I’m using. I’m down to my last two unclued, but my impasse suggests that my crossers for those may be incorrect, so I’ll have another crack in the morning. Certainly a challenge approached the way I'm doing it!

There cannot be 144 different ways to fill the grid bar the unclued entries as that would be impossible to solve without computer

There is 1 way to fill the upper left quadrant, 4 ways for upper right. 8 ways for lower left, 6 for lower right. There are no constraints between them other than no duplicates, and there are fact no dupes. So there are 192 ways to fill the grid ignoring the unclued entries

Does that take into account the anagram element of the puzzle as doubt that would be solvable if that was the case

I think there are 15 different ways to fill the grid bar the unclued entries and the number of pairs of 6-digit numbers (a,b) such that b is a multiple of a and also an anagram of a is 241 but I am not a computing expert. I would be interested to know from one.

buzzb—when you refer to these numbers of ways to fill the quadrants, do you mean including their portions of the unclued answers?

I’ve just started over because I worried I had made a mistake preventing the anagrams from working, and my top left and top right quadrants are filled (NOT including any unclued bits) with, as far as I can tell, the only possible solutions for the clued answers. If top right is in fact variable, I’m worried there’s something I’m not understanding about the puzzle.

buzzb you wrote "There is 1 way to fill the upper left quadrant, 4 ways for upper right. 8 ways for lower left, 6 for lower right."
By my reckoning "There is 1 way to fill the upper left quadrant, 1 way for upper right. 3 ways for lower left, 5 for lower right."

The computing aspect is not really relevant to me, as I don’t write code. But the puzzle is certainly solvable with just a calculator, though the unclued answers take some teasing out. Bananabean’s characterisation is much closer to my experience. Excellent puzzle, thanks to Arden