This month we have a problem from Car Talk and a variant of it.
Draw two straight lines on the face of a clock so that the sum of the numbers in each of the resulting pieces is the same. Note: There are two possibilities: the lines do not intersect and three pieces are formed or they do intersect and four pieces are formed [see below]. Also, this is not a trick question; you are not allowed to "split" a numeral [for example draw the line between the 1 and the 2 in 12].
Source: Car Talk, a weekly radio program on NPR hosted by the Magliozzi brothers, Tom and Ray
Suppose that instead of a 12 hour clock, we have an n hour clock.
For which n is it possible to draw one straight line that divides the clock into two pieces so that the sum of the numbers in each piece are the same?