White is to move. It isn't that hard to find the move that draws, but in two minutes, I couldn't work out the move that wins for White. All other moves are dead losses for White. Solving this puzzle requires basic visualization skills which seem beyond my current capabilities.
Milhouse of course immediately answers 27-23.
Addendum: I should have been able to sort this out. 22-18 obviously loses a checker. 22-17 is the obvious drawing move (although red has to respond with 7-11, responding with the slightly plausible looking 15-18 is a loss, but is fairly tricky to see). 24-19 loses a checker to no good effect. 32-28 bottles up white hopelessly. We are left with 27-23. That forces Red's jump, but he's not going to get the chance to king since white moves to threaten a double jump. To respond to that, Red gives up the checker, and we end up in a symmetric position, but White has the move, and will win.