IMO Shortlist 2010 problem C4

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Dodao/la: arhiva
23. lipnja 2013.
Each of the six boxes B_1, B_2, B_3, B_4, B_5, B_6 initially contains one coin. The following operations are allowed

Type 1) Choose a non-empty box B_j, 1\leq j \leq 5, remove one coin from B_j and add two coins to B_{j+1};

Type 2) Choose a non-empty box B_k, 1\leq k \leq 4, remove one coin from B_k and swap the contents (maybe empty) of the boxes B_{k+1} and B_{k+2}.

Determine if there exists a finite sequence of operations of the allowed types, such that the five boxes B_1, B_2, B_3, B_4, B_5 become empty, while box B_6 contains exactly 2010^{2010^{2010}} coins.

Proposed by Hans Zantema, Netherlands
Izvor: Međunarodna matematička olimpijada, shortlist 2010