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The Reve's Puzzle

The Reve was a wily man and something of a scholar. 
As Chaucer tells us, "There was no auditor could of him win," and "there could no man bring him in arrear." 
The poet also noticed that "ever he rode the hindermost of the route." 
This he did that he might the better, without interruption, work out the fanciful problems and ideas that passed through his active brain. 

When the pilgrims were stopping at a wayside tavern, a number of cheeses of varying sizes caught his alert eye; and calling for four stools, he told the company that he would show them a puzzle of his own that would keep them amused during their rest. 

He then placed eight cheeses of graduating sizes on one of the end stools, the smallest cheese being at the top, as clearly shown in the illustration. 

"This is a riddle," quoth he, "that I did once set before my fellow townsmen at Baldeswell, that is in Norfolk, and, by Saint Joce, there was no man among them that could rede it aright. 
And yet it is withal full easy, for all that I do desire is that, by the moving of one cheese at a time from one stool unto another, ye shall remove all the cheeses to the stool at the other end without ever putting any cheese on one that is smaller than itself. 

To him that will perform this feat in the least number of moves that be possible will I give a draught of the best that our good host can provide." 

To solve this puzzle in the fewest possible moves, first with 8, then with 10, and afterwards with 21 cheeses, is an interesting recreation.

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