This is a solution to You'll Need a Drink After Trying to Solve This Whisky Riddle, part of our Riddle of the Week series.
You'll Need a Drink After Trying to Solve This Whisky Riddle
One way to approach this problem quickly is by thinking in extremes.
Suppose the spoon was the same size as the entire glass. In that case, putting Alan’s “spoonful” of whisky into Claire’s water would entail mixing both glasses together, leading to a mixture that’s half water and half whisky. Then, when Claire returns a “spoonful” of this mixture to Alan’s glass, there would be exactly half water and half whisky in both glasses.
So in this extreme, there would be the same amount of water in Alan’s whisky as there is whisky in Claire’s water. Indeed, this is the solution no matter the size of the spoon.
To answer more carefully, let’s assume each glass has 100 milliliters (mL) of each liquid to start with: Alan’s has 100 mL of whisky and Claire’s has 100 mL of water. Since the liquid transfers consist of removing and adding a spoonful to each glass, the net amount of liquid changed in each glass is zero. Thus, both glasses end with the same amount of liquid they started with: 100 mL.
This means if Alan has x mL of water in his glass at the end, then he must have exactly 100-x mL of whisky. Since we know that there’s 100 mL of whisky in total, this means there must be x mL of whisky in Claire’s glass.
So the water in Alan’s glass must have displaced whisky in Alan’s glass one-for-one, such that there is exactly the same volume of water in Alan’s glass as there is whiskey in Claire’s glass. This will be the case no matter how well Claire mixed!
Laura Feiveson is an economist for the government, a storyteller, and a lifelong enthusiast of math puzzles. She lives in Washington, DC with her husband and two daughters.
