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Nominal Expression Sum (Posted on 2013-09-17) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Solution My faulty p'n'p and successful computer solution. Comment 4 of 4 |

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.

157 is prime, etc.

It looks to me that nothing will better 56.

Now to verify that with a computer program:

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

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

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