Question

Anil has bought a new game, which is in the form of 6 concentric circles.The 6th circle has a radius of 6 and it has 6 openings. A ball is positioned on the circumference of the innermost circle and it finally exits from the circumference of the outermost circle. Thus, the ball starts travelling from the smallest circle 1 and leaves it at the point of opening on the normal to reach the next circle 2, then it moves in a similar manner to 3 and so on.The total number of different paths in which the ball can take to come out of the 6th circle is?

• A. 2⁶*6!
• B. 2⁵*6!
• C. 6!
• D. 2⁵(5)!

Answer 1

The correct option is A

2⁶*6!

There are n openings to come out of the nth circle and it can travel in

the clockwise or anticlockwise direction to enter the (n+1)th circle.

Thus the number of paths is

(1*2)*(2*2)*(3*2)......(6*2) = 6!*2${}^6$

Shortcut

This is a numbers to numbers question.

Use the technique of double substitution

Rewrite the answer options in terms of n as follows,

a) 2${}^n$n! B) 2${}^{n-1}$*n! c) n! d) 2${}^{n-1}$(n -1)! e) 2${}^{n+1}$(n-1)!

Now at n=1, there are 2 ways in which they can exit from the innermost

circle. At n=1 only option (a) gives 2. Answer is option (a)