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The Monks Puzzle

The Monk that went with the party was a great lover of sport.

"Greyhounds he had as swift as fowl of flight: Of riding and of hunting for the hare 

Was all his love, for no cost would he spare." One day he addressed the pilgrims as follows:

"There is a little matter that hath at times perplexed me greatly, though certes it is of no great weight; yet may it serve to try the wits of some that be cunning in such things. 
Nine kennels have I for the use of my dogs, and they be put in the form of a square; though the one in the middle I do never use, it not being of a useful nature. 

Now the riddle is to find in how many different ways I may place my dogs in all or any of the outside kennels so that the number of dogs on every side of the square may be just ten.

The small diagrams show four ways of doing it, and though the fourth way is merely a reversal of the third, it counts as different. 

Any kennels may be left empty. 




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