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Subj:.....The Cheese Problem (S633)           From the book               "Mathematical Puzzles of Sam Loyd"            Edited by Martin Gardner            From: Dover Publications in 1959   How many pieces of cheese did the soldier produce with six cuts? The theme for a good puzzle can be suggested by anything striking or novel that one chances to see, but the appli- cation or proper working out of the scheme may require considerable time and study.  Something in the ordinary affairs of life puzzles us a little by its oddity, and the thought naturally occurs, "If this thing perplexed me in its accidental form, when no feature of difficulty was intended, how would it be possible to increase the difficulty by dressing it up in true puzzle form so as to conceal the principle involved?" The problem must be posed pleasantly, so that the picture aids in explaining the terms and at the same time conceals its real difficulty by imparting what Bret Harte would term a "childlike and bland" simplicity to the whole story. The very name may be utilized to draw attention away from the trick, for, as an old philosopher remarked several centuries before spoke United States, "Ars est celare artem," by which he meant to inform puzzle-makers that the true art is to conceal the art.  Therein lies the main difference between modern and old time puzzles. Changing one day to be in an army commissary department when an assistant was portioning out cheese, I was struck by the ingenious way in which he divided it.  The more I thought it over the more firmly I became convinced that here was a happy suggestion which would eventually crystal- ize into puzzle form.  I complimented the quartermaster upon the skill of his assistant, to which he replied: "Oh, that is nothing!  You should see him cut pie!" The cutting of a piece of pie pertains only to the surface, going no further than square roots or second powers, as the mathematician would say.  In the portioning of cheese we go below the surface into cubic equations known as the third power, for we have to consider the feature of depth. Can you tell how many pieces are produced by the following six straight cuts?

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