Problem 447. swap sign sum & multiply castles

Created by AMITAVA BISWAS

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<ul><li>It is an easy problem, if you know the answer.</li><li>Given a square matrix of NxN ordinary numbers.</li><li>Initially place N identical indistinguishable castles or rooks (chess pieces) on the main diagonal.</li><li>Then keep swapping any two rows or columns to exhaustively enumerate all possible unique patterns of castle formation.</li><li>Not a single castle in any of these formations should be under threat of any other castle,</li><li>only one castle watches over an otherwise empty row and column.</li><li>For each pattern, find the product of all numbers covered by the castles.</li><li>If this pattern was obtained after even number (0,2,4,...) of swaps,</li><li>then add the product to an initially empty accumulator,</li><li>otherwise subtract the product from the accumulator.</li><li>Give the final expected value of the accumulator,</li><li>does not matter whether by hook or by crook,</li><li>but please give a general solution,</li><li>the test suite may be modified soon.</li></ul>

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Problem 447. swap sign sum & multiply castles

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