Forum:Numbers from question 5 of IMO2010

See here first, this game can lead large numbers.

If we have 6 boxes containing 1 coin each, we can make first 5 boxes empty and the last one contain 2*2^(2^^(2^^(2^14))) coins.

More detailed, we can make [a,0] to [0,2a], make [a,0,0] to [0,2^a,0], make [a,0,0,0] to [0,2^^a,0,0], and so on.

If we have n boxes containing 1 coin each, then do operations to make the first n-1 boxes empty, how many coins can we get in the last one? The maximum of it may have growth rate comparable to \(f_{\omega}(n)\). hyp$hyp?cos&#38;cos (talk) 02:36, February 12, 2014 (UTC)