Starting with the 2 in the centre, the number 2005 can be formed by moving from circle to circle only if the two circles are touching. How many different paths can be followed to form 2005?
(A) 36
(B) 24
(C) 12
(D) 18
(E) 6

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-112.jpg?height=244&width=282&top_left_y=211&top_left_x=1279)
From the 2 in the centre, there are 6 possible 0 s to which we can move.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-204.jpg?height=254&width=304&top_left_y=1529&top_left_x=954)

From any 0 , there are 2 possible 0 s to which we can move.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-204.jpg?height=258&width=287&top_left_y=1931&top_left_x=968)

From any 0 , there are 3 possible 5 s to which we can move.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-204.jpg?height=247&width=271&top_left_y=2332&top_left_x=970)

For each of the 6 choices of the first 0 , we can choose either of the 2 choices for the second 0 , and from whichever second 0 is chosen we can choose any of the 3 possible 5 s.

Therefore, there are $6 \times 2 \times 3=36$ possible paths that can be followed.

ANSWER: (A)