A harder variant. Five identical empty buckets of capacity $b$ stand at the vertices of a regular pentagon. Cinderella and her wicked Stepmother go through a sequence of rounds: At the beginning of every round, the Stepmother takes one liter of water from the nearby river and distributes it arbitrarily over the five buckets. Then Cinderella chooses a pair of neighboring buckets, empties them into the river, and puts them back. Then the next round begins. The Stepmother's goal is to make one of these buckets overflow. Cinderella's goal is to prevent this. Determine all bucket capacities $b$ for which the Stepmother can enforce a bucket to overflow.
Solution to the harder variant. The answer is $b<2$.
The previous proof shows that for all $b \geq 2$ the Stepmother cannot enforce overflowing. Now if $b<2$, let $R$ be a positive integer such that $b<2-2^{1-R}$. In the first $R$ rounds the Stepmother now ensures that at least one of the (nonadjacent) buckets $B_{1}$ and $B_{3}$ have contents of at least $1-2^{1-r}$ at the beginning of round $r(r=1,2, \ldots, R)$. This is trivial for $r=1$ and if it holds at the beginning of round $r$, she can fill the bucket which contains at least $1-2^{1-r}$ liters with another $2^{-r}$ liters and put the rest of her water $-1-2^{-r}$ liters - in the other bucket. As Cinderella now can remove the water of at most one of the two buckets, the other bucket carries its contents into the next round.
At the beginning of the $R$-th round there are $1-2^{1-R}$ liters in $B_{1}$ or $B_{3}$. The Stepmother puts the entire liter into that bucket and produces an overflow since $b<2-2^{1-R}$.