I'm a computer programmer trainer and sometimes I do some puzzle exercises with my students. Right now we did a checkers game and I would like to make them program to solve something with their checkers board. Do you know any interesting puzzle?
Using a program, find a series of checkers turns that result in the original position, but with all kings, (use the regular setup of checkers in the start)
Use a program you made to find how many kings you can place on a checkers board where each king can legally capture exactly 2 pieces? Or is this even possible?
Some other ideas are finding zugzwangs or forced ties with the minimal or maximum number of pieces. Maybe minimal for one side and maximum for the other.
You could also give them a couple of pre-set boards and tell them to find the steps taken by either side to ensure a win. That might turn into some sort of branching tree, so you'd have to be careful with the starting positions to ensure both an optimal strategy and not make it too complex.