# Problem 447. swap sign sum & multiply castles

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

### Solution Stats

46.34% Correct | 53.66% Incorrect
Last Solution submitted on Apr 17, 2024

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