Question 15
Luffy and five crewmen sit in a circle to divide $99$ gold coins. Luffy chooses his share and each crewman’s share. Each crewman votes yes exactly when his share is greater than both neighbors’ shares. A majority of the five crewmen must vote yes for Luffy to survive. What is the greatest share Luffy can take? Shares are nonnegative integers; a person may receive zero coins.