Points, Lines & Planes · Challenge problem

Six points $A_1, A_2, \ldots, A_6$ lie on a line in that order, with $A_1A_2 = 1$, $A_2A_3 = 2$, $A_3A_4 = 3$, $A_4A_5 = 4$, and $A_5A_6 = 5$. Of the $15$ segments whose endpoints are two of these points, how many have even length?