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The number of solutions $\left ( x, y, z \right )$ to the equation $x-y-z=25$, where $x, y,$ and $z$ are positive integers such that $x\leq 40,y\leq 12,$ and $z\leq 12,$ is 

  1. $101$
  2. $99$
  3. $87$
  4. $105$
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