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I agree with that. At the very least, if it wanted to go down that line, the preamble could have said “each expressed uniquely using three digits” as Cockie suggested @4, but I would have removed all reference to the rule

Thank you to all who have offered guidance on what to enter under the grid.

Your pointers have made me realise I was massively over complicating things, and I really should have spotted what was going on a lot quicker. Now that the penny has dropped I can see how neatly everything ends up being.

A lovely puzzle that I very much enjoyed solving. Thanks Elap.

Do the numbers below the grid have any significance in themselves, thematically or otherwise? I agree that “relates to the rule for the sequence” is confusing. Also, if one has properly filled the grid, aren’t the sums redundant? Is the consensus that we should apply only the second, third and fourth words of the message? Or do we need to do something with respect to the last word of the message?

My advice is to forget the message and just see if you can come up with a way of expressing the totals with three digits

Thanks. I agree that “expressed in a three-digit form” (full stop) is all the information one needs, without reference to the rule.

Hi all
Perhaps someone could clarify?
The preamble states that no entry starts with a zero.
Is it possible for a letter to represent a number starting with a zero?
For example 48 is divisible by 3 and gives 2304 as its square. The last two digits are 04. Could a letter represent 04?
Thanks

No.

It couldn't be clearer! Thanks cockie!

Enjoyed completing the grid, and deciphering the message.

I have created a series comprising 27 of the clued entries and 1 unclued entry, but I have 4 clued entries and 1 unclued entry left over.

Weird.

Anyhow, thanks Elap for a very clever and entertaining puzzle.

I had this at first. Try using the method on one of the unused ones.