Problem:
Let be the vertices of a regular dodecagon. How many distinct squares in the plane of the dodecagon have at least two vertices in the set ?
Solution:
Each pair of the pairs of vertices generates three squares, one having diagonal , and the other two having as a side. However, each of the three squares , and is counted six times. The total number of squares is therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions