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Thanks Buzzybee - so it has more than one black square, contradicting the first instruction? Or am I missing something?

SirC
The first instruction says that each FACE has a black square in the middle. The 3×3 block referred to is not a face - it is the middle row of the cube, which has letters at its corners only.

You need to think in 3d. If all those blocks were put together to make a cube you would have a cube with just one black square in the middle of each fa e

Indeed CandleD. Might be helpful to visualise these cubes like a Rubiks cube with 3 letter words along the edges.

actually I found the idea of a cube confusing - I had to cut the squares out and align them in three layers

as it's still not on the Guardian site, I assume there's no way of submitting ...

Thanks jono for the puzzle.

I posted the link at Gdn 'comments' section.

@Moaljodad responded:

Think I'll hold fire on this - looks like it needs a final once-over by the editor before it's ready for publication...

Very neat idea and nowhere near as difficult as the preamble might have suggested. Thanks to Pangakupu. However, no thanks to the Grauniad. One can only hope that it appears on the site before the apparent deadline of 3 December. (shome mishtake shurely? ed.)

The main crossword was, for once, easy. The preamble is certainly confusing (where does a five come in?). The sixteen words are in the four corners of the crossword. Trying to work out which are the other eight unnecessary words, and which synonym one should use is not so easy. But are some of the four corner "cubes" to be applied upside-down?

Bah. Still not getting it. This might be a 2-dayer/sleep-on-itter for me.

I can easily imagine a Rubik's cube with the 24 3 letter answers on the outer edges. No problem there.

But if that's the case why does the preamble describe 2 cubes?

How can the sandwich filling have four black squares, then, miraculously, just the one, when I imagine it in the round?

Don't try to help me. I'm beyond help and have already cracked open a soothing drink.

Panga as a bear with a sore head with myself....

ps please do enjoy your well-deserved smugness, the finishers, to whom I proffer my agonies as a sauce