Let’s start with the brothers having equal amounts, work backwards to the will, and forwards again to the alternative situation.

Let’s say they ended with £x each. The final round is Adam’s, so immediately prior to that they would have:

A 2x

B x/2

C x/2

Then Barnaby’s share is doubled and the other two decrease by the 1/2 of what Barnaby had:

A 7x/4

B x

C x/4

Then Charles:

A 13x/8

B 7x/8

C x/2

To check we haven’t gone wrong, at each stage the amount should add up to 3x, since we are only moving money between the brothers.

Next we need to move forward from this point with the alternative order.

First Adam splits his share such that his share is halved and 1/4 of what Adam had is added to each of the others:

A 13x/16

B 41x/32

C 29x/32

Then Barnaby splits his share:

A 145x/128

B 41x/64

C 157x/128

And finally Charles:

A 737x/512

B 485x/512

C 157x/256

We are told that in this scenario Adam ends up with £19881 more than Charles, so:

737x/512 – 157x/256 = 19881

x(737-314) = 19881*512

x = 24064

Then going back to the will scenario (13x/8 etc) we can say that the will granted the following amounts:

Adam: £39,104

Barnaby: £21,056

Charles: £12,032