﻿Given the following constraint satisfaction problem, determine whether a solution exists:

Variables: x, y, z, each taking values from {1, 2, 3}
Constraints:
  C1: x != y
  C2: y != z
  C3: z != x
  C4: x + y + z = 4
  C5: x >= y
  C6: y >= z

Find all solutions, or prove that none exist. If unsatisfiable, provide a minimal explanation of which constraints conflict.
