Nosey Parker

Probability Level 4

It is Valentine's Day, and a mathematician is going to visit his girlfriend.

The mathematician's home is on the bottom left corner of the grid, and his girlfriend lives at the top right corner. He has to stop by the flower shop at F-S to get a bouquet of flowers for his girlfriend. From S, he will go on to her house. However, he wants to avoid N-P for that is where his Nosey Parker friend lives, and if he passes by N-P, his friend will pull him into his house for a very long chat and he will not be able to visit his girlfriend. :(.

Find the number of shortest routes that the mathematician can take to his girlfriend's house.

This problem is an entry in the Valentine's Day Contest .

The answer is 2292.

1 solution

Nicole Tay
Feb 20, 2016

Home to F-S: $\huge(\frac{4}{2!2!})$

S to Girlfriend's House: $\huge(\frac{11}{5!6!})$

S to N-P to House: $\huge(\frac{4!}{1!3!})$ $\huge(\frac{6!}{3!3!})$

Number of Shortest Routes: $\huge(\frac{4}{2!2!})$ * ( $\huge(\frac{11}{5!6!})$ - $\huge(\frac{4!}{1!3!})$ $\huge(\frac{6!}{3!3!})$ ) = 2292

Nosey Parker

This problem is an entry in the Valentine's Day Contest .

The answer is 2292.

1 solution

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