Chittagong Secondary 2017#4
Posted: Sat Feb 24, 2018 1:52 am
In a $2015×2$ chess board,what is the maximum number of horses we can put such that no horses attack each other?
The Official Online Forum of BdMO
https://matholympiad.org.bd/forum/
Sorry brother,your solution is not right .It doesn't mean that if there are 2015 black squares then there can be placed 2015 horses at the maximum rate.First think about 5*2 chessboard.You can put at most 4 horses in 5*2 chessboard such that no horse attack each other.Then add up 403 such chessboards to get a 2015*2 chessboard.So you can put at most 403*4=1612 horses in 2015*2 chessboard which meets the given condition.
Akash7 wrote: ↑Wed May 02, 2018 8:03 pmWHY ?? I can put 5 knights in that boat.samiul_samin wrote: ↑Sat Feb 24, 2018 1:53 am.First think about 5*2 chessboard.You can put at most 4 horses in 5*2 chessboard .
Both of us was wrong .Akash7 wrote: ↑Wed May 02, 2018 8:03 pmSorry brother,your solution is not right .It doesn't mean that if there are 2015 black squares then there can be placed 2015 horses at the maximum rate.First think about 5*2 chessboard.You can put at most 4 horses in 5*2 chessboard such that no horse attack each other.Then add up 403 such chessboards to get a 2015*2 chessboard.So you can put at most 403*4=1612 horses in 2015*2 chessboard which meets the given condition.