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Find the number of non-negative integral solutions: |x+y|+|w+z|=10. How does one approach this problem?
I need to find the number of non-negative integral solutions for |x+y|+|w+z|=10. How should I approach this problem?
To solve this problem, you can use the concept of partitioning. First, consider the case when x + y and w + z are non-negative. Then, you can partition the 10 into 5 pairs of 2 and count the number of ways to distribute each pair to x+y and w+z using the stars and bars method. Afterwards, you can consider the cases when x + y or w + z is negative and use similar partitioning and counting methods.