Course Solutions Uncategorized (Solved) : Cinderella Stepmother Problem Two Player Game Cinderella Stepmother Take Turns Take Action Q34272267 . . . .

(Solved) : Cinderella Stepmother Problem Two Player Game Cinderella Stepmother Take Turns Take Action Q34272267 . . . .

 

The Cinderella-Stepmother problem is a two-player game, in which Cinderella and Stepmother take turns to take actions. Cinderella has 4 water buckets, initially empty, arranged in a circle. In each turn, Cinderella first chooses to empty 2 adjacent buckets. Afterwards, Stepmother adds up to 4 liters of water to the buckets, and can distribute the water arbitrarily over the buckets in multiples of 1 liter of water. After Stepmothers action, the game proceeds to the next turn. Every bucket has a capacity of 8 liters, and it is Cinderellas objective to avoid any bucket being overflown. Figure 2 shows 

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