Is there a clever solution to Arnold's "merchant problem"?
Solution 1:
At the end the tea cup is as full as at the start. This implies that the added wine is exactly outweighed by the tea that has disappeared.
Solution 2:
The volume of spoon, $s$, is the conserved quantity. It is also the amount of wine in the cup.
When you then take some mixture $\mathit{tea}+\mathit{wine} = s$ into the spoon,
$s-\mathit{wine}$ is the amount of wine left in the cup and the amount of tea poured into the wine barrel.