A mathematics challenge based on excessive, pointless politeness. Are you ready?
I have one glass full of something. You have an identical glass, but it's empty. I'm in a sharing mood; I pour half of the contents of my glass into yours. You repay my generosity by pouring half of your glass' contents into mine, in addition to what's already in there. And then I pour half of mine into yours... If this comedy of manners keeps going, with each of us in turn pouring half of our glass into the other's, will we ever reach an equilibrium cycle? How many turns will the cycle have, and which values?
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