The mystery of the boardinghouse pie

Puzzle

As showing how mathematics may be discussed in a digestible form, let us look into the following unique problem, which comes in with the new regime introduced by the recently formed Pie Trust: It having come to the knowledge of the Boarders' Protective Union that the chef of Madame O'Flaharity's Pension Francais was cutting too many pieces out of one pie, which conflicts with Article V. of the by-laws, which says: "A union pie must be divided with six straight cuts of a .knife, the walking delegates of the association ordered a strike among the boarders until the grievance was corrected. The sketch shows the madame explaining the limit of possibilities in dividing a No. 6 union pie, which problem will appeal directly to the hearts of the American pie-loving people irrespective of the beauty and importance of the proposition from a mathematical standpoint. Madame O'Flaharity is discoursing upon the advantages of extending the greatest possible latitude to the practical application of the six-straight-cut-rule which affords anopportunity of varying the size and number of pieces according to circumstances. As a matter of fact, the opportunity for dispensing pieces of pie of variable size is generally utilized to advantage by clever landladies who have mastered the problem. The star boarders, and such as pay their bills promptly, get the big pieces with plenty of nice crust, while such as are badly in arrears get frozen out, so far as pie is concerned. And what a volume of sentiment and appreciation can be expressed by the large thick piece which the hostess serves to the young doctor who is supposed to be attentive to her daughter Mary Jane!

Puzzle in short

Into how many pieces, of various sizes, is it possible to divide a pie with six straight cuts of a knife?

Solution

Answer

The boardinghouse pie can be cut into 22 pieces, as shown. The letters show how Aunt Mary marked her pies so as to tell whether 'tis mince or 'taint mince:

References

• Loyd, Sam [1914]. in Loyd, Sam, Jr.: Sam Loyd's Cyclopedia of 5000 Puzzles Tricks and Conundrums (in English). New York: Lamb Publishing company, page 18.