July 10th, 2003, 10:14 AM

Sums and constraints
Hi there,
straight to the problem:
 We can only use numbers from 1 to 4.
 We have a sum p to reach, as large as we want
 We have a max number of addends s, as large as we want
 We have to calculate the min addend and the max addend we have to use to reach the sum, if it is ever possible to be reached.
Note: we can take no care of commutation: a+b === b+a
Example 1:
s = 2
p = 4
Possible sums: (2+2, 1+3)
So solution is: (1, 3)
Example 2:
s = 3
p = 6
Possible sums: (2+2+2, 4+1+1, 3+2+1)
So solution is: (1, 4)
Example 3:
s = 3
p = 2
No solution, impossible problem
I'd like to get this automagically.
I filled a table with the first few rows and columns and I noticed we get a diagonal matrix., since we cannot have a solution when s > p
Hope to have been clear.
I wait for your opinions.
Bye and thanx!