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Coffee and Milk (illustration)
FILE No.142Unsolved

Coffee and Milk

Difficulty ★★☆about 5 minLogic PuzzleConservationSymmetry
You mix one spoonful of milk into coffee, then return a spoonful of the mixture. Which is greater?

Case Record

There is a cup of coffee and a cup of milk with equal amounts. First, put one spoonful of milk into the coffee and mix well. Then scoop one spoonful of the mixture from the coffee cup and return it to the milk cup.

Your question

Which is greater: "the coffee mixed into the milk cup" or "the milk mixed into the coffee cup"?

Case Files

Diagram

Coffee and milk (same amount)CoffeeMilk1) 1 spoon of milk2) 1 spoon of the mix1) Put 1 spoon of milk into the coffee and mix well. 2) Return 1 spoon ofthe mixture to the milk cup.Which is more: coffee in the milk cup, or milk in the coffee cup?
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

At the end, is each cup's amount the same as at first?

Open hint 2

Where is the milk that left the milk cup?

Open hint 3

Compare the amount that went out with the amount that came in.

Solve It

Your question

Which is greater: "the coffee mixed into the milk cup" or "the milk mixed into the coffee cup"?

Choose the answer closest to the truth.

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The Truth

They are the same

The answer is "They are the same."

In the end, both cups return to their original amounts. The amount of milk that left the milk cup and the amount of coffee that entered it cannot help but be equal.

Even if the mixing differs, the final amounts do not change, so "it depends on how it is mixed" is wrong.

What goes in balances what comes outCupFinal amountSoMilk cupBack to the originalMilk lost = coffee gainedCoffee cupBack to the originalCoffee lost = milk gainedCoffee in the milk cup equals milk in the coffee cup, however it ismixed.
Diagram of the solution

Key Points

  • Notice that the final amounts return to the originals
  • What went out = what came in
  • No detailed calculation is needed

Why people get fooled

Because you try to calculate the mixed ratios and get lost.

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