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Grid now completed and word discovered (with special thanks to Unclued)

Does anyone understand why 15 across refers to "at least half"? Surely it is half or more than half. Seems rather vague to me.

"At least half" is precise, here meaning "4, 5, 6, 7 or 8". That's not as helpful as saying "exactly 4" but it isn't vague.

Would dearly appreciate some help with this...

Firstly, are the first 2 digits of 11a. 1, 5?

Secondly, is the 'segmenting into 3 numbers, where one of them is the sum of the other two' achieved by dividing them into 3 double digit numbers as outlined below?

For example, if 11a. was 1,5,8,2 - then would the 3 segmented no.'s would be 15 - 58 - 82.

It's just I can't find any 2 no's that follow 1 and 5 (Excluding 3,4,7 and 0) that when split into 3, as above, meet the criteria. Obviously 1 might not be the first number but I've checked 1d. 3 times now and every time get the same answer, namely one where 1 is the middle number.

Hi Brendan,
You are correct with your first two figures for 11a. The answer to your second question is no.
Say, for example, if 11a was 1248 (which it can't be obviously), you could segment it into 12, 4, 8. 12 is the sum of 4 and 8.

Thank you so much Cloverjo, that was slowly driving me insane.