Kinesys materializes in the middle of a lavishly set table: on Staterion, the Feast of Fairness is underway, where every guest must receive exactly the same amount of everything. The scales, naturally, sit among the dishes.
A waiter places two carafes in front of the crew: one with a quart of water, the other with a quart of wine. Then, with a precision spoon, he starts moving tiny amounts from one to the other.
“This is an assault on order,” Dord protests. “Now neither carafe is pure!” Liz, who only wanted a glass of water, sighs. M00N, however, is fascinated: “I wonder who came out ahead, the water or the wine?”
The Riddle
There are two carafes, one containing a quart of water and the other a quart of wine. A teaspoon of water is moved into the wine carafe, and the wine and water are mixed thoroughly. Then a teaspoon of the mixture is moved back into the water carafe. Is there now more water in the wine than wine in the water? Or the other way around?
Hint
Don’t get distracted by the numbers or the mixing. At the end, how much liquid is in each carafe? Think about what takes the place of the wine that left its carafe.
Solution
The answer is that there is as much wine in the water as there is water in the wine.
The fun part of this problem is the extraordinary amount of irrelevant information. You don’t need to know how much liquid is in each carafe, how much is transferred, or how many transfers are made. It doesn’t even matter whether the mixtures are well mixed or not, or whether the two containers start out with the same amount of liquid.
The only condition that matters is that at the end each carafe holds exactly the same amount of liquid it held at the start. In that case, if an amount x of wine is missing from the wine carafe, the space that wine used to occupy must now be occupied by an amount x of water. And the missing wine is, of course, in the water carafe.