Lemonink Puzzle - Solution

The Puzzle:

Lemonink
I have two glasses the same size. One contains 100 ml of lemonade and the other contains 100 ml of ink.



I take a spoonful of lemonade and stir it into the ink, and then take a spoonful of that mixture and stir it back into the lemonade.

Which glass now contains least of the contents of the other one?




Our Solution:

The actual answer was that BOTH glasses contained the same amount of the other liquid in them.

Each glass ends up with 100ml of liquid in it, as before, but the first glass (lemonade) has some of the lemonade replaced by ink, and this bit of lemonade can be found in the second glass (ink) where it is replacing the same amount of ink. Gettit?


For those who doubt this, imagine you transfer 10ml each time. We will use [100,0] to mean "100ml of Lemonade, 0ml of Ink":
Start: [100,0], [0,100]
Transfer 10ml: [90,0], [10,100]
Mix, and take 10 ml from 2nd glass, which will be 1/11th Lemonade (round it to 0.909ml)
Transfer [0.909, 9.091] back: [90.909, 9.091], [9.091,90.909]


Puzzle Author: Stephen Froggatt

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