Love For MathCreative Math Education

Help the bee find its way!

Problems ·

The initial position of a Bee is shown in the Beehive.

It can move in only one general direction, namely, to the right. For example, if the bee was in cell H, it could move only to I or J from there.

In how many ways can the bee reach the cell ‘D’ from the starting point?

In how many ways can the bee reach the the cell ‘H’from the starting point?

Can you suggest a way to determine, the number of ways in which the bee can reach any cell from the starting point?

What students worked out16

  • Student 27

    Love the Fibonacci, don’t you?

    • Karanteacher

      Absolutely love it! I wonder why is it a Fibonacci sequence though! Can you explain that?

  • Student 16

    Bee can reach cell D via paths:BD;
    ABD;
    ACD Three ways

    • Student 16

      It needs modification :
      Bee can reach cell D via paths:BD;
      ABD;
      ACD ;
      ABCD : Four ways

  • Student 16

    Next problem to reach cell H:
    paths BDFH;
    ABDFH;ABCDEFGH;
    ACDFH;ACDEFGH;ACEFH; ACEFGH;ACEGH;
    eight ways

    • Student 22

      There are more than eight ways. You can also reach BDFGH, BDEFH, BDEFGH, BDEGH, BCDFH, BCDFGH, BCDEFH, BCDEFGH, BCDEGH, BCEFH, BCEFGH, BCEGH and so on

  • Student 22

    A,B,C,D,E,F,G,H are replaced by 1,2,3 and so on, then the general answer to reach position n can written as follows

    2^n if n is even
    2*n-1 if n is odd

    • Student 22

      CORRECTION
      2^(n/2) if n is even
      2^((n-1)/2)+1 if n is odd

    • Student 22

      CORRECTION
      Its will be following Fibonacci Sequence
      A,B,C,D,E,F,G,H,I,J,… will be 1,2,3,5,8,13,21,34,55,89, ….

      • Karanteacher

        That’s generalized very well. Can we take it to next level and think about why is this making a Fibonacci sequence?

  • Student 33

    The bee can go through cell B to reach cell D. The bee can go through the cells B, D and F from the starting point to reach cell H. The bee can reach cell O via cells: B, D, F, H, J, L and N.

  • Student 51

    3

  • Student 49

    It will reach in 4 ways to reach D
    BD, ABCD, BCD, ABD.
     
    To reach H, it will TAKE many ways
    ABCDEFGH, BDFH, BCDEFGH, ACEFH, ACEFH, ACEFH, ABDFH, etc…

    • Karanteacher

      It seems that you missed out something in counting ways to reach D.
       
      Also, can you find how many total would be there for H?

  • Student 48

    1.b,d
    2.a,c,d
    3.b,c,d
    4.a,b,d
    5.b,a,c,d

  • Student 47

    1.b,d
    2.a,c,d
    3.b,c,d
    4.a,b,d
    5.b,a,c,d