2025 Cayley Problem 18

Lavinia has one bottle with capacity 6 L and another bottle with capacity 5 L. Both bottles are empty. She has a piece of paper with the following steps printed on it:

(i) Fill the 6 L bottle completely with water.

(ii) Pour water from the 6 L bottle into the 5 L bottle until the 5 L bottle is full.

(iii) Empty the 5 L bottle.

(iv) Pour water from the 6 L bottle into the 5 L bottle until the 5 L bottle is full or the 6 L bottle is empty, whichever happens first. If the 5 L bottle fills, empty the 5 L bottle and return to the beginning of this step.

Lavinia completes this sequence of four steps in this order a total of 3 times. Lavinia never spills any water. How much water will be in the 5 L bottle after Lavinia is finished?

\textbf{(A)}\ 0 \text{ L}\quad \textbf{(B)}\ 1 \text{ L}\quad \textbf{(C)}\ 2 \text{ L}\quad \textbf{(D)}\ 3 \text{ L}\quad \textbf{(E)}\ 4 \text{ L}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.