I have two glasses, one containing precisely 12 fluid ounces of coffee, the other containing precisely 12 fluid ounces of tea.
I pour one fluid ounce from the coffee cup into the tea cup, and then thoroughly mix the contents. I then pour one fluid ounce from the (mostly) tea cup back into the coffee cup, and then thoroughly mix the contents. Is there more coffee in the tea cup, or more tea in the coffee cup?
In this Classic case, after transferring 1 ounce of coffee to the tea cup, it would have 1 ounce of coffee and 12 ounces of tea. Once thoroughly mixed, each ounce of the liquid would have $1/13$ ounce of coffee and $12/13$ ounce of tea in it. So after moving one ounce back to the coffe cup, the coffee cup would have $11+1/13=144/13$ ounces of coffee and $12/13$ ounces of tea. Conversely, the tea cup would have $1-1/13=12/13$ ounces of coffee and $12-12/13=144/13$ ounces of tea. So after one mixing back and forth the volume of tea in the coffee cup is equal to the volume of coffee in the tea cup.
