re: It isn't the exercise....
Several times, I've solved my most difficult programming problems while asleep. I've had problems in programs that defied discovery no matter how hard I worked, only to "see" the problem on the exact line of code at 2 AM. Sure enough, I'd look at the code in the morning and there would be the bug exactly where my sleeping mind pointed out. Sometimes, you just have to know when to back off and let the solution reveal itself.