If the number of plants in the circle is (2^n) where n is any integer then all flowers turn red after sufficient number of days irrespective of the initial arrangement.

Its difficult to describe the full method here. But I am giving you pointers which will easily lead to the solution.

You can assign 0 to white and 1 to red.

First you can show that principle of superposition is valid. For example, you can split a case with k red flowers into k seperate cases each having only one red flower at appropriate position and analyse. After going forward by say, p number of days, you can again superpose the k cases so that you get the original thing.

This makes the problem easy. Now we can analyse the "one flower red" case in detail.

After analysing this case in detail, you will observe the following.
After (2^k) days, only (2^k)th flowers on either of the sides of the original red flower are red. So if the (2^k)th positions on left and right coincide, then by superposition, all the flowers will become white.

This shows that the number of flowers has to be (2^k)

Its not so straightforward. Put a little thinking into this and you will get what I want to say

Go back to the problem.

Back to main page