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?

(In reply to Simplified, no solution by Jer)

Even though Jer's simplification significantly reduces the burden of solving analytically, one will still be left with 95 simple sets  of equations like:

(i) y+z =k      k<95,
(ii) G = 2y + 5*(k-y)   each set creating a subset of possible G,

then creating the union of various solutions to avoid duplicity and then returning to linear translation  to get H.

Clearly, this is a proper puzzle for a heuristic exhaustive program and any shortcuts are not needed.
 

Posted by Ady TZIDON on 2014-10-16 13:20:08