Knight's Tour Latin Squares I
I bet you are wondering what the heck does Knight's Tours have to do with Latin Squares. Well, you might just be surprised to find out that Knight's Tours can make amazing Latin Squares. Before I forget, I guess I should define what a Latin Square is for those that do not know. As seen in one of my other Knight's Tour webpages, a dictionary definition might be confusing.
"noun
plural noun: Latin squares
For the purpose of this webpage, let's use the following Wikipedia definition that applies more accurately.
Therefore, for our purpose, a Latin Square contains a series of numbers from 1-8 or 2-9 that when placed in an 8x8 grid square, no numbers repeat themselves in the same row or the same column. Here is an example:
"noun
plural noun: Latin squares
- an arrangement of letters or symbols that each occur n times, in a square array of n 2 compartments so that no letter appears twice in the same row or column.
- a Latin square used as the basis of experimental procedures in which it is desired to control or allow for two sources of variability while investigating a third."
For the purpose of this webpage, let's use the following Wikipedia definition that applies more accurately.
- "In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column."
Therefore, for our purpose, a Latin Square contains a series of numbers from 1-8 or 2-9 that when placed in an 8x8 grid square, no numbers repeat themselves in the same row or the same column. Here is an example:
Latin Square - Magic Constant 36
Take a look at the following Knight's Tour Latin Square puzzles.
Puzzle-1 - Knight's Tour Latin Square
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Puzzle-2 - Knight's Tour Latin Square
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Try solving the Knight's Tour Latin Square puzzles shown above. Hint, after solving the squares, you should be able to draw four separate 16-Move Closed Knight's Tours in each square. If you are unable to solve the problems, click on the Knight's Tour Latin Squares above to see their S-O-L-U-T-I-O-N.