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If the bank security codes are cash machine PIN numbers then 3d + 15d should be 1967 or higher (when cash machines first appeared in the UK) but that's a big assumption to make, I admit. One of my two possibilities for 15d would give a date post 1967.

What are we to make of the Time Travel department and its implications?

Murky, what do 3d & 15d have to do with security codes?

1a is a 2-digit factor of 14d which is product of three 2-digit primes. Consequently 1a must be one of those primes.

Carpox1, if the message was written in the future, then 15d could be greater than 2018 - 3d.

I should say that aspects of the Great Quad, 6ac and 5d, emerged quite easily once I had the second digit of 3d. However, I'm struggling with the Lesser Quad.

1a does not imply that 15d is greater than 201. He could be writing in the 1700s and have access to future information from the time travel department. This would be an error by the setter.

It would only be an error by the setter, if that led to an alternative grid fill that perfectly satisfies all the clues. For example, assuming time travel, 15d might be 169 but based on what demeter posted that apparently leads to a dead end.

I meant if assuming 15d was greater than 201 was what the setter intended us to conclude in order to complete the puzzle, then he would have made an error.

Buzzb, the sum of 3d and 15d equals the date of the setting of the puzzle. I was positing an assumption that the date would be 1967 or later.

However, the reference to a Time Travel department does rather complicate things.

Unless I have 22ac wrong, I think there are only 3 options for 14d. One of those has a prime that I think is too large for any of the entries where it might go.

Thanks, Murky, for your comment about the introduction of ATMs. I think that's key to the puzzle. It gave me 15d, hence 1ac, then, with 15 ac, 2ac etc - it all worked out very quickly after that

Dylan, I'm pleased it helped, though I haven't finished myself yet. I thought that 2d could only be one figure to make things work out for the snail clues, but it has so many factors that it's no help in determining the second digit of 13d. I have 3 possibilities for 16a, and the resulting entries for 13d would all have very few factors.

As someone said earlier, it's that dratted snail.