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Thread: Need help please

  1. #1
    Apr 2006

    Need help please

    My daughter age 11 can't do this, and I can't help her. Could someone explain very basically how to solve it please.

    Many thanks


    Draw an X and Y plan, with the coordinates of O being your origin (0,0). Plot A with coordinates (2,0), B (3,0) and C (2,1).

    Now in this question journeys are made of steps of whole-numbers length in any combination of directions left, right, up or down. Also one may retrace steps. So, for example, it is possible to travel from O to the point (2,1) by journey OAC which has length 3, it is possible to get to (2,1) by a different journey, OBAC which has length 5.

    a) Starting from O, how many possible destinations (including O) are there with journeys of length

    1) 2?
    2) 3?

    b) How many different journeys of length 3 are there starting at O and finishing at (1,0)?

    c) You are given that the sum 1+2+3+....+100 = 5050
    How many journeys of length 102 are there from O to coordinate (100,0)?
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  2. #2
    MHF Contributor
    Apr 2008
    For (a), the only point from A, B, C reachable in only two steps is A. You can also go from O to O by moving a step in one direction and then moving back to O.

    You cannot go from O to O or from O to A in three steps (why?). However, you can go to B or C in exactly three steps for both.

    For (b), you can get to (1, 0) in one step. It is therefore possible to get to (1, 0) in three steps by including one direction and its opposite (up, down, for instance). Also, you must take into account that each possible combination of moves (up, down, right, for example) can be done in any order, and each possible order is a different journey. Finally, there must always be a move to the right.

    For (c), use the same trick you did for (b). Since you can get to (100, 0) in 100 moves, if you use 102 moves you can include one direction and its opposite in addition to 100 moves to the right.
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