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Math Help - Number of blocks possible?

  1. #1
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    Number of blocks possible?

    A city has a grid pattern, with 10 streets running north/south and 20 streets running east/west. What is the mimimum numver of blocks you have to walk to get from the the northwest corner to the southeast corner. How many ways can you get there walking this minimum number of blocks?


    I assume the minimum is 30. How would you solve this problem? Could you do 10 choose 1 and 20 choose 1 and end up with 300?
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  2. #2
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    Quote Originally Posted by taylor1234 View Post
    A city has a grid pattern, with 10 streets running north/south and 20 streets running east/west. What is the mimimum numver of blocks you have to walk to get from the the northwest corner to the southeast corner. How many ways can you get there walking this minimum number of blocks?


    I assume the minimum is 30. How would you solve this problem? Could you do 10 choose 1 and 20 choose 1 and end up with 300?
    I think the number of blocks is 28 and you can get the answer by considering permutations of the multiset {0,0,...,0,1,1,...,1} where there are 9 zeroes and 19 ones. The number I get is 6906900.
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