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This thread is aimed at those needing a little extra assistance. If you're struggling - really struggling! - post here and someone may be able to help. As it's a numerical puzzle, which I never attempt, I don't know how revealing it would be to give actual answers. I'm sure Forum members will manage somehow.

Thanks Malone. As this is a numerical puzzle, I will hold over on posting the three threads until next week.

I have run up against an early brick wall. I have found what I believe to be all the initial possibilities for 4ac/18dn (4-digit powers) and likewise for 7dn (2-digit powers) , which lead me to only one match for the intersection of 4ac/7dn. But when I then turn to 18dn (the other 4-digit power) and add this to 7dn, so as to solve 6dn, I hit my brick wall.
I can only assume that some 2-digit or 4-digit powers are escaping me but I'm blowed if I can see what they are.

Moffat, you have definitely found the way into the puzzle. My combinations work OK. I have three possible values for both 4ac and 7dn. Only one combination works in conjunction with 18dn.

moffat -

You said "I have found what I believe to be all the initial possibilities for 4ac/18dn (4-digit powers) and likewise for 7dn (2-digit powers) , which lead me to only one match for the intersection of 4ac/7dn."

There are in fact 2 matches for the intersection of 4ac/7dn as there are two choices for 4a that end in the same digit as the leading digit for one of the choices for 7d

Thank you chums. Needless to say, soon after posting I discovered my missing cube, and now I'm in and moving.

I've done 4a,. 18d, 6d, 7d, 14a, 15d, 19a, 32d. Now stuck. Where next please?

Forgot, done 29a too

I went to 22d next which gave me 21a then slogged away until 18a emerged.

Thanks a million Panicea.