IMO Shortlist 2014 problem C2
Kvaliteta:
Avg: 3.0Težina:
Avg: 6.0We have sheets of paper, with the number
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
and
, then we erase these numbers and write the number
on both sheets. Prove that after
steps, the sum of the numbers on all the sheets is at least
.
(Iran)
Source: https://www.imo-official.org/problems/IMO2014SL.pdf