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1. Let w, x, y, and z belong to the complete set of integers. If each of wxy + z^2, wxz + y^2, wyz + x^2, xyz + w^2 is divisible by 4, show that w^3 + x^3 + y^3 + z^3 is divisible by 4.
2. Let w, x, y, and z belong to the complete set of integers. If each of wxy + z^2, wxz + y^2, wyz + x^2, xyz + w^2 is divisible by 4, show that w^3 + x^3 + y^3 + z^3 is divisible by 4.
3. 9(9 - 9)! = 9
4. Please ignore the prior post. Let the remaining matchsticks be located at these coordinates on the xy-axes: (0, 0) to (0, 1) (0, 1) to (0, 2) (0, 2) to (0, 3) (2, 0) to (2, 1) (2, 1) to (2, 2) (2, 2) to (2, 3) (3, 1) to (3, 2) (3, 2) to (3, 3) (0, 0) to (1, 0) (1, 0) to (2, 0) (0, 1) to (1, 1) (1, 1) to (2, 1) (2, 1) to (3, 1) (0, 2) to (1, 2) (1, 2) to (2, 2) (2, 2) to (3, 2) (0, 3) to (1, 3) (1, 3) to (2, 3)
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