SOLUTION: Two sides of a regular n-gon, when extended meet at an angle 42 degrees. What is the least possible value of n?

The smallest angle between the sides of regular polygon is the exterior angle
of the regular polygon, which is 360/n degrees.


Any angle between other sides of the regular polygon is a multiple of this 
minimal angle, i.e. is a multiple of 360/n degrees.


Thus to find the least possible value of n, we should select least possible 
value of n sich that 42 degrees is a multiple of 360/n.


Since 42 = 6*7 and 360 = 6*60, such least possible value of n  is 60.


Thus n = 60.


ANSWER.  n = 60.