# Pig pigsty

In response to the repeated question of how puzzles originate, whether from a sudden inspiration or as a result of a long and careful study, I would say that just like the development of any other invention come from both origins, from a thought happy and hard work although in any case the idea is generally suggested by some opportunistic and casual event.

As an example I will say that during my summer excursion while touring the country on wheels I found an affable place where an apple orchard, fresh spring water, a small shack and its friendly tenant made a true Mecca for the tired pilgrims in bike.

It had a unique character and was an inexhaustible source of anecdotes. He was interested in knowing the reason why I immortalized him in print when he saw the drawing I made of him sitting in his characteristic posture at the door of his home. The original image, perfectly framed, I sent it to decorate his "living room" in gratitude for the puzzle he suggested

It seems that there was a certain bond of communion between us since our lives were always linked to the pigsty. He asked me if I knew why an Irishman always builds a pigsty by the living room window? After I had suggested lots of explanations and completely exhausted my repertoire of witty comments, he told me in a confidential whisper that he could be heard a mile that was built there to keep the pigs inside.

During the trip back home I fell off the bike a dozen times thinking about Pat's problem. There was a comment about his pigsty that I found curious and is that he used odd numbers to organize his piara. It seems that Pat has made her own rule for breeding, only twenty-one pigs each season. To accommodate them, he built the pigsty by the living room window, dividing his happy family into four fences, so that each one contains an even number of couples plus a solitary pig.

It seems an easy problem to divide twenty-one pigs that way quickly, you can try it!

If you understand the mystery of Shakespeare in "the divinity of odd numbers," show how Pat arranged his twenty-one pigs in four fences so that each one contains the odd number of pigs mentioned.

In summary
Divide the pigsty into 4 fences so that each one contains an even number of couples plus a loose pig.

#### Solution

The problem of Pat's pig pigsty perplexed many intelligent mathematicians and puzzle enthusiasts who failed to place the twenty-one pigs in four pens so that there were an odd number of pigs inside each fence with an even number of couples.

Smart fans suggested the need to use the “nesting” of the fences within each other, but the requirement that each fence must contain “an even number of couples”, as well as the fact that the outer fence should contain At least five pigs had spoiled some of the suggested answers.

The only possible answer is to place five pigs in the center fence, that is, two pairs and one loose.

Then build a fence that surrounds it and place four pigs in it, a third that surrounds both also with four pigs and the last one, with eight pigs, encloses the other fences. In this way, all twenty-one pigs are included as shown in the following image.