The author provides an example of obtaining the correct answer to a problem through a so-called nonsense solution. The conditions under which this incorrect method will yield a correct solution are examined. (JP)

Non-traditional methods of presenting and solving calculus problems in high school mathematics classes are presented. All problems deal with the principle that the maximum product of two numbers whose sum is constant is obtained if the numbers are equal (i.e., the arithmetic mean of n numbers is greater than or equal to the geometric mean). (JG)

The author presents a variation of a tiling problem where each row or column contains a complete set of elements, each diagonal is free of contiguous like elements, and at least one partition exists. These restrictions limit the number of solutions considerably, and methods of solution are subsequently discussed. (CT)

Discussion is focused on standard teaching procedures that contain the elements of modern mathematics. Of the various methods which have been tested, it is concluded that the solving of problems remains the most effective basic activity. A sample collection of problems is presented to indicate relationships and the principles they illustrate. (RP)