Regional 2016 set 6 Higher Secondary P 7

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samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
Regional 2016 set 6 Higher Secondary P 7

Unread post by samiul_samin » Sun Feb 17, 2019 8:42 pm

In a $100x100$ chess board, a pawn is placed in the lowest row, $50^{th}$ box from the left. A pawn can only move one box straight or diagonally in forward direction. The pawn is moved for $20$ times. What is the maximum number of box where can this pawn be? [Count the initial position too]

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: Regional 2016 set 6 Higher Secondary P 7

Unread post by samiul_samin » Sun Feb 17, 2019 8:46 pm

Hint
This is a tricky counting problem
Answer
$441$
Solution
We can understand the problem if we draw a chess board.
Maximum number of box$=1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39+41=441$

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