A probability question i think

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In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally upward and to the right. How many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard?


Thanks in advance for helping me!

  • A probability question i think -

    Each move advances either upward or rightward or both. If there are n diagonal moves, then there are 14-n up or right moves. So, there may be 0 to 7 diagonal moves, and the rest can be chosen in two ways.

    so, there are

    (0+2^14) + (1+2^12) + (2+2^10) + ... + (7+0) = 21872

  • A probability question i think -

    ok thanks alot steve you really help alot

  • A probability question i think -

    steve is wrong...

  • A probability question i think -

    You are wrong

  • A probability question i think -

    You guys....actually try to help out please.

    Here, make a chart that cascades to the upper-right-most square. Kinda like Pascal's Triangle.

    1............. 48639
    1...................
    1...................
    1...................
    1 7 25..............
    1 5 13 .............
    1 3 5 7 9...........
    1 1 1 1 1 1 1 1 1 1 1

    So the answer is 48639.

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