ROSECODE 127
Crazy World Cup
World cup 2014 got crazier then ever.
Each new day a new team registers to world cup with an insane match schedule. Team registered at day i dictates that they will only be able to play i days and then they will take rest for i days after and this pattern will continue on.
In an example team registered at day 1 will have an availability schedule like:
10101010..... (where 1 denotes available)
Availability for Team registered in day 2:
011001100.....
Availability for Team registered in day 3:
00111000111.....
So on and so forth...
The administration wants to match up all teams at ith day. So, number of available teams at day i must be even to do that.
The question is just for mathematical enthusiasm and it may make no sense. So, how many days will NOT be valid for such a matching if the world cup lasted for 10^18 days?
Each new day a new team registers to world cup with an insane match schedule. Team registered at day i dictates that they will only be able to play i days and then they will take rest for i days after and this pattern will continue on.
In an example team registered at day 1 will have an availability schedule like:
10101010..... (where 1 denotes available)
Availability for Team registered in day 2:
011001100.....
Availability for Team registered in day 3:
00111000111.....
So on and so forth...
The administration wants to match up all teams at ith day. So, number of available teams at day i must be even to do that.
The question is just for mathematical enthusiasm and it may make no sense. So, how many days will NOT be valid for such a matching if the world cup lasted for 10^18 days?