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#### veronica1999

##### Member

- Jun 4, 2012

- 63

line with exactly 100 feet between adjacent gates. His departure gate is

assigned at random. After waiting at that gate, Dave is told the departure

gate has been changed to a different gate, again at random. Let the

probability that Dave walks 400 feet or less to the new gate be a fraction

m/n , where m and n are relatively prime positive integers. Find m + n .

I got the answer 52 but I am not that happy with my solution.

(I think I solved it using brute force because the problem was simple)

Can someone show me a better way?

Total choices are 12X11.

I listed all the gates and tried each one out.

4+5 +6 + 7 +8 + 8 +8 +8 +7 + 6 +5 +4 = 76

76/121 = 19/33

Thanks.