IMO Shortlist 2014 problem C2


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7. svibnja 2017.
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We have 2^m sheets of paper, with the number 1 written on each of them. We perform the following operation. In every step we choose two distinct sheets; if the numbers on the two sheets are a and b, then we erase these numbers and write the number a + b on both sheets. Prove that after m 2^{m-1} steps, the sum of the numbers on all the sheets is at least 4^m.

(Iran)

Izvor: https://www.imo-official.org/problems/IMO2014SL.pdf