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.

This competition closed on Sunday 20th January 2019.

The entries

There was again a good number of entries for this competition. Nearly all entrants ended up with the correct answer, albeit with a variety of slightly different approaches.

The solution

A solution as provided by our winner was:

The total number of possible arrangements of 16 items is 16!

However, we are only interested in arrangements where the orders for each letter are constrained to decrease from 4 to 1 i.e. A4..A3..A2..A1

thus we divide by 4! for each letter.

= 16! / (4! x 4! X 4! X 4!)

= 63,063,000

And the winner is...

J Brown, a technical analyst with a PhD in Remote Sensing from the University of Cambridge, is the winner of ECM's Brainbuster no. 44 competition.

... winning £200 of Amazon vouchers to spend on high-tech. Congratulations again to our winner, and watch out for ecm's next brainbuster!