|Spoiler Inside: Solution to Puzzle||SelectShow>|
One could start from the largest unit and work down, but there is a short-cut.
Two of each of the denominations adds up to 273 pence. The short way is to figure out all of the ways that one can make change for 273 – 240 = 33 pence using up to two of each denomination and subtract the number of each denomination used from two.
The combinations adding totalling 33d. are (with blanks meaning 0):
The subtractions from two of each denomination are obvious.
There are nine ways to make change.