Mixing Day - Futility Closet

Mixing Day

A puzzle from P.M.H. Kendall and G.M. Thomas’ Mathematical Puzzles for the Connoisseur (1962):

Start with two containers, one holding green paint and the other an equal quantity of red paint.

Pour one pint of green paint into the red.
Pour two pints of this mixture back into the green.
Pour half the mixture in the green paint pot into the red pot.

Assume the paints are mixed thoroughly after each operation. If the two containers are now leveled off, without pouring any paint away, so that they both contain an equal quantity of paint, which pot is now more pure, the “green” paint or the “red”?

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They’re equally pure. This is a fun puzzle because you can put the solver through any ludicrous number of operations and the answer is always the same. If we start and end with the same total quantity of paint in each pot, then any paint lost from the first pot must be replaced with paint from the second, and vice versa.

July 29, 2016August 7, 2016 | Puzzles