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It a new chess game is invented which ha...

It a new chess game is invented which has 9 x 9 grid, tiled by 81 squares of size `1 xx 1`, in chess board pattern, instead of 8 x 8 and rule is that in a single step the king can only move along horizontal orver tical to the adjacent tile. If king is at the center tile of this grid then find total number of shortest path she can take to reach at any corner of chess board ?

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(i) Find the number of reatangles of any size in a chess board (ii) Find the number of squares of any size in a rectangle of size 8xx 5 .

(i) Find the number of reatangles of any size in a chess board (ii) Find the number of squares of any size in a rectangle of size 8xx 5 .