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?**

1.b,d

2.a,c,d

3.b,c,d

4.a,b,d

5.b,a,c,d

1.b,d

2.a,c,d

3.b,c,d

4.a,b,d

5.b,a,c,d

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…

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?3

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.

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

CORRECTION

2^(n/2) if n is even

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

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, ….

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

Next problem to reach cell H:

paths BDFH;

ABDFH;ABCDEFGH;

ACDFH;ACDEFGH;ACEFH; ACEFGH;ACEGH;

eight ways

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

Bee can reach cell D via paths:BD;

ABD;

ACD Three ways

It needs modification :

Bee can reach cell D via paths:BD;

ABD;

ACD ;

ABCD : Four ways

Love the Fibonacci, don’t you?

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