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National and Regional Contests
Iran Contests
Iran MO (1st Round)
2018 Iran MO (1st Round)
5
5
Part of
2018 Iran MO (1st Round)
Problems
(1)
COVID hits the palaestra - Iran First Round 2018, P5
Source:
3/6/2021
There are
128
128
128
numbered seats arranged around a circle in a palaestra. The first person to enter the place would sit on seat number
1
1
1
. Since a contagious disease is infecting the people of the city, each person who enters the palaestra would sit on a seat whose distance is the longest to the nearest occupied seat. If there are several such seats, the newly entered person would sit on the seat with the smallest number. What is the number of the seat on which the
39
39
39
th person sits?
combinatorics
Covid-19