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Distinct Values Validation (Posted on 2014-10-16) Difficulty: 3 of 5
Each of x, y and z is a nonnegative integer such that:

(i) x+y+z = 94, and:
(ii) H = 4x+10y+19z

How many distinct values of H is possible?

No Solution Yet Submitted by K Sengupta    
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Hints/Tips Simplified, no solution | Comment 1 of 7
We can simplify things talking 4 away from each of x, y and z, since this will remove 94 4's.
H = 0x + 6y + 15z + 4*94
(H-376) = 6y + 15z
(H-376)/3 = 2y + 5z
Call G = (H-376)/3 and we can rephrase the conditions and question as the equivalent:

(i) y+z ≤94, and:
(ii) G = 2y + 5z

How many distinct values of G is (sic) possible?

Edited on October 17, 2014, 6:45 am
  Posted by Jer on 2014-10-16 10:16:51

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