swap sign sum & multiply castles - MATLAB Cody - MATLAB Central

Problem 447. swap sign sum & multiply castles

Difficulty:Rate
  • 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

51.96% Correct | 48.04% Incorrect
Last Solution submitted on Oct 08, 2025

Problem Comments

Solution Comments

Show comments
MATLAB EXPO 2025 Registration is Now Open! November 12 – 13, 2025
Registration is now open for MathWorks annual virtual event MATLAB EXPO 2025...
0

Problem Recent Solvers90

Suggested Problems

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!