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The mystery of the pension cake

The mystery of the pension cake

To demonstrate how mathematics can be discussed in a digestible way let's take a look at the following problem that arises with the new regime introduced by the recently constituted "reality of the cake": It is known by all that the Chef of the French pension of the Mrs. O'Flaharity has cut too many pieces of a cake which conflicts with article V of the statutes that says: “A union must divide the cake with six straight cuts of a knife. The association delegates ordered a strike between attendees until the claim was addressed. The drawing shows the lady who explains the limit of the possibilities in the division of the cake, a problem that alludes directly to the hearts of cake lovers regardless of the beauty and importance of the proposal from a mathematical point of view.

Madame O'Flaharity is discussing the advantages of extending to the maximum possible latitude the practical application of the rule of the six straight cuts that provides the opportunity to vary the size and number of portions according to the circumstances.

In fact, the possibility of getting pieces of cake of variable size is generally used as a virtue by the ladies who dominate the problem.

In summary, How many different sized portions can you divide the cake with six straight knife cuts?

Solution

The cake can be cut into 22 pieces, as shown in the following illustration: