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Pascals Triangle (Checkerboard Question)

  1. Dec 3, 2012 #1
    Hello,

    I'm a little confused as to how I can go about solving this problem.. Any help is appreciated.

    1. The problem statement, all variables and given/known data

    Draw and copy the following checkerboard. Then, on the board, show all of the paths that the checker piece can take to reach the bottom square marked with an “X,” without going through the two blacked-out squares. Remember, the checker piece can only move diagonally forwards by one square at a time, in this case, using the white squares only. How many paths are there in total?





    3. The attempt at a solution

    In my answer I got 8 as the number of paths to reach the bottom square marked with an "X". Is this correct?

    Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 3, 2012 #2

    symbolipoint

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    I only find TWO paths to reach the X. The first move has exactly two choices. The remaining choices will all be along the same diagonal direction to reach the X white square. Your condition includes moving FORWARD only. If you deviate away from the main diagonal path straight to the X, then you will miss the X.
     
  4. Dec 3, 2012 #3
    So your saying this would be the correct method?
     

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  5. Dec 3, 2012 #4

    Mentallic

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    Those squares with the 4's and 6, and that 2 on the right wall nearest to the bottom need to be removed. You can't land on those squares and still reach the X.
     
  6. Dec 3, 2012 #5
    Sorry guys, I dont know if its just me or what but I'm still not getting this :S
     
  7. Dec 4, 2012 #6

    Mentallic

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    There isn't much to get. When you get to the second square (either by first moving left or right), there is only 1 way to get to the X from that position and that is by moving diagonally straight towards it.
     
  8. Dec 4, 2012 #7
    So essentially x would be.. 2?
     
  9. Dec 4, 2012 #8

    symbolipoint

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    That number for categorizing the labeled squares seems to fit. What you have wanted to know was how many paths are possible for reaching the square labeled "X". That answer is, two paths.
     
  10. Dec 4, 2012 #9
    Ah man, guess I need to read the question properly next time! Thanks!
     
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