If all the 9 edges along length and breadth of a chess board are the tracks, then how many ways

M4maths Previous Puzzles

11 Mar 2010 Shortest Track?

If all the 9 edges along length and breadth of a chess board are the tracks, then how many ways
are possible for a man to reach the diagonally opposite point starting from a corner in shortest track.

OPtion

(1) 12870
(2) 12012
(3) 10296
(4) 13728
(5) 32760
(6) 64
(7) 120
(8) 1024
(9) 256
(10) 143432

Solution

Total number of part tracks required for reaching the destination from a corner are 16 in which 8 are along length and 8 are along breadth
Number of methods for choosing the track are
(16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1)2
= 12870

Correct Option: 1 Best Solution (3)