Each of A, B, C and D is a positive integer, with A > B, such that: A+B = C - 11*D.

Determine (with proof) the quadruplet (A, B, C, D) that generates the minimum value of A+B+C+D. What quadruplet generates the next smallest value of A+B+C+D?

A>B, let A=2, B=1, they can't be smaller. Let D=1; again, it can't be smaller.

Then 3=C-11 and C=14; 14+2+1+1=18.

If we increase B, B=A, so increase A: A=3, B=1, the next smallest values. Let D=1; it can't be smaller. 4=C-11 and C=15; 15+3+1+1=20

So these are the smallest solutions.

Posted by broll on 2011-04-07 02:38:25