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.
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