## 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!