Statistics, Data Analysis and Probability for Grade 12, Problem ID: 5406
Anton, the highest IQ house ant on the planet, is taking his regular nocturnal walk from one corner of the chess board (1,1) to the diagonally opposite corner (8,8), moving only right or up the board at each successive square. He remembers that on square (5,3) there is a 'black-hole', so any valid route must exclude this square.
From how many different paths can he choose?
[HINT: You could try an easier problem first.]
Author: Leslie Green
16! / (8!)2 - (8!) / (3!)14! / (7!)2 - (7!) / (3!)14! / (7!)2 - (5!) / (3!)16! / (8!)2 - (8!) / (5!)