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The Sompnour's Puzzle

 The Sompnour, or Summoner, who, according to Chaucer, joined the party of pilgrims, was an officer whose duty was to summon delinquents to appear in ecclesiastical courts.  In later times he became known as the apparitor.  Our particular individual was a somewhat quaint though worthy man.  "He was a gentle hireling and a kind; A better fellow should a man not find."  In order that the reader may understand his appearance in the picture, it must be explained that his peculiar headgear is duly recorded by the poet.  "A garland had he set upon his head, As great as if it were for an ale-stake." One evening ten of the company stopped at a village inn and requested to be put up for the night, but mine host could only accommodate five of them.  The Sompnour suggested that they should draw lots, and as he had had experience in such matters in the summoning of juries and in other ways, he arranged the company in a circle and proposed a "count out."  Being of a chivalrous nature, his little plot was so to arrange that the men should all fall out and leave the ladies in possession.  He therefore gave the Wife of Bath a number and directed her to count round and round the circle, in a clockwise direction, and the person on whom that number fell was immediately to step out of the ring.  The count then began afresh at the next person.  But the lady misunderstood her instructions, and selected in mistake the number eleven and started the count at herself.  As will be found, this resulted in all the women falling out in turn instead of the men, for every eleventh person withdrawn from the circle is a lady. "Of a truth it was no fault of mine," said the Sompnour next day to the company, "and herein is methinks a riddle.  Can anyone tell me what number the good Wife should have used withal, and at which pilgrim she should have begun her count so that no other than the five men should have been counted out?"  Of course, the point is to find the smallest number that will have the desired effect. See answer

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