Magical Pond!


I have to visit three temples T1, T2 and T3, and offer flowers at each temple. I pluck the flowers from my garden. The temples are far away from my home and, so, I cannot come back for flowers every time. I have to pluck as many flowers as I need only once.

There are two rules I have to follow: (1) I cannot visit just one temple; I must visit all the three. (2) I must offer flowers at each temple - it does not matter how many I offer but I must offer the same number of flowers in each temple.

There is a magical pond in front of each temple. Let's call these ponds P1, P2 and P3. Pond P1 is in front of temple T1, P2 in front of temple T2, and P3 in front of temple T3.

Now these ponds are magical. When you dip flowers in them, they get doubled. For instance, if you dip, say, five flowers in any of the ponds, then you get back ten flowers!

Well, I carried a certain number of flowers after plucking them from my garden. I dipped all of them in P1 and got back double the number of flowers. Then, I offered a certain number of flowers (out of the total flowers that I had) in the first temple T1.

Next, I dipped all the flowers left with me in P2. Hey presto, the number of flowers doubled! Then, I offered the same number of flowers that I had offered in T1 in temple T2 also. That left me with few flowers when I exited Temple T2.

All these remaining flowers I dipped in P3 and got double the number of flowers. I offered all these flowers in temple T3, and not a single flower was left with me when I exited T3. Of course, the number of flowers offered in T3 was the same as that offered in T1 and T2.

Can you tell me how many flowers I plucked from the garden, and how many did I offer in each temple? To make things clearer, let's say I had plucked "x" flowers and offered "y" number of flowers in each temple.

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