From Mathcounts Mini :
Counting/Paths Along a Grid
From Art of Problem Solving
Counting Paths on a Grid
Math Principles : Paths on a Grid : Two Approaches
Question #1: How many ways to move the dominoes on a 6 by 6 checker board if you can only move the dominoes to the right or to the bottom starting from the upper left and you can't move the dominoes diagonally?
Solution :
You can move the dominoes 5 times to the right at most and 5 down to
the bottom at most, so the answer is (5+5)!5!×5! = 252 ways
Question # 2: How many ways can you move from A to B if you can only move downward and to right?
Solution :
There are (4+4)!4!×4! * 2 * (4+4)!4!×4! = 9800 ways from A to B
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