knights and rooks:puzzleup2014

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Knights and Rooks

Knights and Rooks

In how many different ways can two knights and two rooks be placed on a standard chessboard so that no one attacks the others? If this question had been asked for a 4×4 board than the answer would be 88. Four of those are as follows.

This list shows the result for a 4×4 table. 0 represents the rook and 1 represents the knight. The second item of (a,b) is the cell position in the table. The first cell is at the 0th position, the last cell is at the 15th. For example, the last output (1,3),(1,7),(0,8),(0,13) tells me the one of the knigts is located at the 3rd cell, which means the first row and the last column, and the other knight is located at the second row and the last column.

What about the algorithm?

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Published by chessmusings

Chris Torres is a nationally renowned scholastic chess coach working in both Bakersfield and the San Francisco Bay Area. His classes have attracted players of strengths ranging from rank beginners to world champions. A chess professional since 1998, Chris is widely recognized as one of the main driving forces behind the explosion in popularity and sudden rise in quality of scholastic chess in California. Currently, Chris Torres has the ranking of candidate master and serves as the President of the Torres Chess and Music Academy. Mr. Torres’ hobbies include playing classical guitar and getting his students to appear on the national top 100 chess rating lists.

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