MathDB

The

2016

players in the Gensokyo Tennis Club are playing Up and Down the River. The players first randomly form

1008

pairs, and each pair is assigned to a tennis court (The courts are numbered from

1

1008

). Every day, the two players on the same court play a match against each other to determine a winner and a loser. For

2\le i\le 1008

, the winner on court

i

will move to court

i-1

the next day (and the winner on court

1

does not move). Likewise, for

1\le j\le 1007

, the loser on court

j

will move to court

j+1

the next day (and the loser on court

1008

does not move). On Day

1

, Reimu is playing on court

123

and Marisa is playing on court

876

. Find the smallest positive integer value of

n

for which it is possible that Reimu and Marisa play one another on Day

n

.
Proposed by Yannick Yao

Problem Statement