Variation of the dining philosophers: is the standard solution still valid?
If the philosopher eats (holding both forks), drops the right fork and thinks for a while, and then drops the left fork to take a nap (or something similar), it is just the original problem: Each philosopher must ensure getting both forks without deadlock. Take a look at Allen B. Downey's "The Little Book on Semaphores" for in-depth discussion (this problem is hard!).