The thesis that selective problem solving can be a vital factor in learning mathematics needs no extended defense. It is implicit in the suggestion by some curriculum experts that problems be made the central point of topical development. A good problem, like the acorn, has in it the potential for grand development.

The Committee on High School Contests, guided by this thesis, seeks through the Annual High School Mathematics Examination—jointly sponsored by the Mathematical Association of America and the Society of Actuaries—to extend, to supplement, and to enrich the regular school work by providing interesting, rewarding, and challenging problems within a prescribed scope.

There is one very important respect in which this competition differs from the Olympiads of Europe and similarly-motivated competitions in the United States and Canada. This competition aims to discriminate on several levels, and is not exclusively directed to high-ability students.

Since the publication of the contest problems through 1960 (NML volume 5), participation in this contest has increased by 100,000 students in the United States and Canada to its present 250,000 from 7000 schools. There is also a fairly large European participation.

Some of the solutions are intentionally incomplete but crucial steps are shown. The exhibited solutions are by no means the only ones possible, nor are they necessarily superior to ail alternatives. Since it is our intention that no mathematics beyond intermediate algebra be required we consistently show an elementary procedure even where a “high-powered” alternative is given.