The brainbuster

Find the solution to this brainbuster and win £200 of Amazon vouchers to spend on high-tech!

An engineer at ACME Software needs to delete four groups of files - A, B, C and D - each consisting of four files:

A1 A2 A3 A4

B1 B2 B3 B4

C1 C2 C3 C4

D1 D2 D3 D4

But there is a constraint: within each group of files the highest numbered file must be deleted first.

So, one way to start would be to delete the highest numbered file from each group: A4 B4 C4 D4 A3 B3 ...

Or a whole group first: C4 C3 C2 C1 A4 A3 ...

Or a more random approach, such as: B4 C4 C3 D4 B3 B2 ...

Evidently there are lots of different ways to delete the 16 files. How many?

Show your workings. Only complete entry forms will be considered. The judge's decision is final.

The competition closes on Sunday 20th January 2019.