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# presidentabrahamlincoln

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## Posts posted by presidentabrahamlincoln

1. ### Show 4 divides this algebraic expression.

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. ### Show an algebraic expression is divisible by 4.

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. ### A Nine Puzzle

9(9 - 9)! = 9

4. ### matchstick puzzle

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)

5. ### matchstick puzzle

On ‎12‎/‎1‎/‎2015 at 8:13 AM, bonanova said:

Any other solutions?

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