Mathematics 1501                                     Calculus I                                     Fall, 2001

The current contest

Some past contests - fame and fortune still await the solvers!

  1. Reuleaux polygons.

    Determine the area of the Reuleaux triangle and the Reuleaux pentagon. These figures are like the usual regular polygons, except that their edges are arcs of a circle, of radius 1. The center of the circle will be at one of the other corners. (Solution.)

  2. The infidelity contest.

    Note: This logic puzzle is the creation of John Allen Paulos, and was recounted in his book Once upon a Number, which was chosen by the Los Angeles Times as one of the best nonfiction books of 1998. The innovation of alien genders is, however, my own.

    A nominally monogamous species on the planet Thrae consists of two genders, "wen" and "momen," the singulars being "wan" and "moman." Now, wen are very intelligent and logical, and each wan knows that all the other wen are equally so. They have the following well-known habits. 1. If a wan has proof that the moman to whom the wan is married has been unfaithful, the wan will kill the moman within one day. 2. Wen's intuition always allows them to know when another wan's spouse has been unfaithful. 3. Wen never tell any wan else about infidelity. 4. For some reason, wen's intuition fails them as to their own spouses. 5. Every wan takes as proved whatever is printed in the Equinchet, a local oracle.

    In the village of Chetag there are forty married couples, and all the momen have been unfaithful. Of course, every wan lives in the belief of being the one wan with a faithful spouse. Well, maybe. One day the Equinchet prints the statement that it has evidence that at least one moman in Chetag has been unfaithful.

    Does any wan learn anything not already known? Do any killings ensue? If so, how many and when? To win this one, you have to have the correct answer and the correct logical reasons for it. (Hint: One wins when one wonders well when one wan wonders whether one wan's one wanders.)

  3. The UGA math contest.

    Over in Athens, Georgia, many people - far, far too many - believe that the derivative of (f g) is f' g' . We all know that the the UGA product ruls is an incorrect rule. But just a a broken watch will tell the correct time twice a day, the UGA product rule will occasionally be correct. For instance, if f and g are constants, it is correct.

    Tha constest is to find as many creative examples where the rule is correct as you can.

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