# What is the simplest way to represent this situation mathematically?

Sitting in my room with two large jars full of green tea and black coffee, I suddenly realized that I would not be able to drink the coffee first. That is because I only regularly drink out of one of the jars. Yet I also realized that, without a third jar, I would not be able to move all of the contents of jar 1 into jar 2. As such, it seemed like there was something universal about the fact that, given two full jars, the contents of one cannot be poured into the other without the existence of a third jar. I suddenly found myself wanting a mathematical abstraction that could represent this situation. But I have no idea how a set could be called 'full.' I suppose there is some set-theoretic mathematical structure that can have this property though, right?

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Sound like Towers of Hanoi. Or variable swap; too bad you can't xor your mugs! – Raphael Sep 25 '11 at 12:47
Also sounds Pigeonhole principle-ish. – Adam Saltz Sep 25 '11 at 13:10
I'm not really sure about set theoretic, more of a combinatorical nature perhaps. In set theory it is the content of the jar that matters; not its name. So without loss of generality just swap the labels and get it over with. – Asaf Karagila Sep 25 '11 at 13:21
Why is this question down voted? Seems to be a sensible question. – Dinesh Sep 25 '11 at 16:14
If it were a jar of water and a jar of sugar, you might be able to pour the contents of one into the other... – Rahul Sep 25 '11 at 20:14