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So I've solved the left hand grid which suggests which clues apply to the right hand grid (except for one of them) but I'm pretty sure I can prove there is no possible solution for the right hand grid, which suggests there may be another solution to the left hand grid? Has anyone else experienced this?

Not I, Astone. The RHS grid fell out quite quickly for me, once I'd done the LHS. I put it down to having established the "groove" of the puzzle by then.

With luck, you've made a small mistake somewhere, because it would be very tedious if there really were two possibilities for the LHS!

I totally get what you mean about getting stuck on one part of the grid sometimes stepping away and revisiting it later helps a lot. I usually keep a small notes sheet for tricky cells and possibilities, which makes spotting errors easier. For word-based logic puzzles, I also like using WordFinderTips
to test letter patterns and spot potential solutions quickly. It’s amazing how similar strategies for numbers and words can be!

If my solution is right Astone, the product of the 5 digits in the bottom row of the LH grid is 11,340. If yours matches that, then its likely your LH grid is correct.

Thanks for the encouraging comments. I went back to my LH grid solution and I got it wrong! Back to the spreadsheet... Thie ironyi is, the product of the 5 digits along the bottom row does indeed equal 11340

That's what I found ie there are other Palindromes that are not labelled as such!

Twice I've put this in the bin with a "life is too short" and twice I've pulled it out and gound again to a contradiction. I had two possibilities (both satisfying the useful hints) but could not make either work. I suspect that working out where the final 0s can go might be a good idea, but I'm not sure I still have the will.

I solved this by writing some code and my computer spit out the solution...Can someone explain how it can be solved the 'right' way? What's the entry point and first few steps?

buzzb.

The way in was hinted at in the preamble - namely 3dn = 3ac x 6ac. 6ac has to start with 1otherwise 3ac/3dn can't start with the same digit. Further 6ac can't be triangular 10 or 15 since 10 duplicates a zero ending and 15 is too large a multiplier. That leaves 12 and 14 and 14 is too large a multiplier also.

The Listener website will have a logical pathway that you could have followed and should appear on Friday 13th March.

Interestingly the 13th day of a month is most likely to be a Friday!