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2025 AMC 10B Problem 9

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2025 AMC 10B Problem 9AMC 10 Step by Step
Name:                             Date: October 28, 2026
Basic Counting · difficulty 3 of 5 · about 5 min · position P1-10

How many ordered triples of integers (x,y,z)(x, y, z) satisfy the following system of inequalities?

−x−y−z≤−2−x+y+z≤2x−y+z≤2x+y−z≤2\begin{align*} -x-y-z&\le -2\\ -x+y+z&\le 2\\ x-y+z&\le 2\\ x+y-z&\le 2 \end{align*}

  1. A)44
  2. B)88
  3. C)1111
  4. D)1515
  5. E)1717

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