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Sorry, quixote, yes, the clue numbers have no relevance for the location of entries. Two pairs of across and down entries start in the same square but they are NOT 1A/1D, 2A/D etc.

I found the numbers useful just for keeping tabs on my entries and ruling them in and out as I started to make (slow!) progress.

The block I cannot overcome is that I don't understand "In the completed grid each of the digits 1 to 9 occupies five contiguous cells." I'm missing something obvious here. How do the digits 1 to 9 fit in 5 cells? Doesn't it need 9 cells? Or is it just some of the digits? It is obviously critical to placement of answers but I am getting nowhere. I hope someone can help.

Catkin, what it means is that each of the digits 1 to 9 appears 5 times (there are 45 spaces in the grid). And each set of 5 is contiguous. e.g. all the 1s are connected by edges, and the same for all the 2s, etc. So each set of digits forms a pentamino. It is indeed critical. 7a only has one possible answer, and only one pentamino fits the way the answer has its digits distributed, and it can only actually go in one place in the grid.

Oh Wow! Thanks Quisling. I couldn't see it! Onwards and upwards!

It would have been better to have numbered the grid traditionally (1a, 4a, 6a...) and just labelled the clues A, B, C....That would have avoided needless confusion.

I suggest that we refer to the clues as A1, A2...A7, D1...D7 to avoid confusion.

Agree the clue numbering could be misleading. Separating down from across was helpful but it may have been better to leave them unnumbered and listed only in order of their answers size.
I suspect this crossword started very differently. Several of the unclued entries can be defined by the sum of two primes. It is possible that clues have been removed and clue order randomised to make it more difficult.
In my view it was a tad easy for a Listener and listing all clues - both across and down - in order of size of answer without numbers might have been an option.

Products not sums….

I wonder how many ways one can fill this grid (ignoring digits) with 9 different pentominoes not counting rotations or reflections of the entire grid.

How many ways after applying A7?

... and could you fill a similar 8x8 grid with all 12 pentominoes ?

Crosswhit99, i believe you can.

Note by Admin - deleted at Quisling’s request