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
Problem Comments
-
1 Comment
Robert Wagner
on 16 Feb 2024
??? kannitverstan
Solution Comments
Show commentsProblem Recent Solvers43
Suggested Problems
-
Construct a string from letters and counts
139 Solvers
-
What is the distance from point P(x,y) to the line Ax + By + C = 0?
361 Solvers
-
Getting the indices from a matrix
618 Solvers
-
291 Solvers
-
Flip the vector from right to left
8154 Solvers
More from this Author100
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!