Given that a*b + c = 160, where each of a, b and c are positive integers.

Determine the minimum value of a + b*c.

Extra Challenge: Solve this using only pen and paper.

The smallest c can be is 1, leaving 159=3*53 for a*b giving 56 for a+b*c, regardless of whether we choose 3 or 53 as a or b, which we might suspect would then be the minimum value.

158=2*79
157 is prime, etc.

It looks to me that nothing will better 56.

Now to verify that with a computer program:

DEFDBL A-Z
min = 99999
FOR c = 1 TO 159
  ab = 160 - c
  FOR a = 1 TO ab
    b = ab / a
    IF b = INT(b) THEN
      v = a + b * c
      IF v <= min THEN
        PRINT a; b; c, v
        min = v
      END IF
    END IF
  NEXT
NEXT

finds a better answer: (a,b,c)= (26, 6, 4) yielding 50.

Posted by Charlie on 2013-09-17 13:49:24