Find the number of positive unequal integral solutions of the equation `x+y+z+w=20`.

Explanation

To find the number of positive unequal integral solutions of the equation \( x + y + z + w = 20 \), we can follow these steps:

### Step 1: Understand the Problem
We need to find the number of positive integral solutions for the equation \( x + y + z + w = 20 \) with the condition that \( x, y, z, \) and \( w \) are all different (unequal).

### Step 2: Change of Variables
Since \( x, y, z, w \) are positive integers, we can define new variables to simplify our calculations. Let:
- \( x' = x - 1 \)
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