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Problem of the Week 1233
The Generous Automated Teller Machine
Imagine you have five boxes, B1, B2, B3, B4, B5; and each one contains one coin. You may make moves of the following sort:
What is the largest number of coins you can place in B(5)?
In this form, it appears to be unsolved. I would be interested to know how large you can get. The original contest problem here had six boxes; and that is, of course, more interesting. I posed the case of 5 because, perhaps for that, one can prove what the maximum is. Feel free to send me your values for either version.
Source: Invented by Hans Zantema, problem 5, 2010 International Mathematical Olympiad, Astana, Kazakhstan (July 8, 2010)
I saw it in this very very nice new problem book, Half a Century of Pythagoras Magazine, eds A. van den Brandhof, J. Guichelaar, and A. Jaspers, MAA, 2015.