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IMO Shortlist 1977 problem 6

1977 alg shortlist sustav
Let n be a positive integer. How many integer solutions (i, j, k, l) , \ 1 \leq i, j, k, l \leq n, does the following system of inequalities have:

1 \leq -j + k + l \leq n 1 \leq i - k + l \leq n 1 \leq i - j + l \leq n 1 \leq i + j - k \leq n \ ?

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