FJ and his cows enjoy playing a mental game. They write down the
numbers from 1 to N (1 <= N <= 10) in a certain order and then sum
adjacent numbers to produce a new list with one fewer number. They
repeat this until only a single number is left. For example, one
instance of the game (when N=4) might go like this:
3 1 2 4
4 3 6
7 9
16
Behind FJ's back, the cows have started playing a more difficult
game, in which they try to determine the starting sequence from
only the final total and the number N. Unfortunately, the game is
a bit above FJ's mental arithmetic capabilities.
Write a program to help FJ play the game and keep up with the cows.
BZPRO