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

Problem 447. swap sign sum & multiply castles

Difficulty:
(13)
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.
Solve

Solution Stats

46.93% Correct | 53.07% Incorrect
Last Solution submitted on Mar 03, 2025

Problem Comments

Solution Comments

Show comments

Group

Programování - Cody Image
Programování - Cody
  • 12 Problems
  • 466 Finishers

Problem Recent Solvers70

Problem Tags

arithmetic chess matrix

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Go to top of page