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The Cook's Puzzle

We find that there was a cook among the company; and his services were no doubt at times in great request, "For he could roast and seethe, and broil and fry, And make a mortress and well bake a pie." 

One night when the pilgrims were seated at a country hostelry, about to begin their repast, the cook presented himself at the head of the table that was presided over by the Franklin, and said, "Listen awhile, my masters, while that I do ask ye a riddle, and by Saint Moden it is one that I cannot answer myself withal. 

There be eleven pilgrims seated at this board on which is set a warden pie and a venison pasty, each of which may truly be divided into four parts and no more. 
Now, mark ye, five out of the eleven pilgrims can eat the pie, but will not touch the pasty, while fourwill eat the pasty but turn away from the pie. 
Moreover, the two that do remain be able and willing to eat of either. 
By my halidame, is there any that can tell me in how many different ways the good Franklin may choose whom he will serve?

I will just caution the reader that if he is not careful he will find, when he sees the answer, that he has made a mistake of forty, as all the company did, with the exception of the Clerk of Oxenford, who got it right by accident, through putting down a wrong figure.

Strange to say, while the company perplexed their wits about this riddle the cook played upon them a merry jest. 
In the midst of their deep thinking and hot dispute what should the cunning knave do but stealthily take away both the pie and the pasty.

Then, when hunger made them desire to go on with the repast, finding there was nought upon the table, they called clamorously for the cook.
"My masters," he explained, "seeing you were so deep set in the riddle, I did take them to the next room, where others did eat them with relish ere they had grown cold. 

There be excellent bread and cheese in the pantry."

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