what will be the generalized form of the question given below, if i'll change no.of temples?

Question

There are three temples and 3 wells arranged in an order of 1 well, 1 temple and so on.
The wells doubles the number of flowers when you wash flowers in them and after that you offer some flowers to the gods in the temple. Assuming you offer the same number of flowers in each temple, how many flowers should you start with that you are left with no flowers after you offer them at the last temple.

Answer:
You start with 7 flowers, double them and make them 14. Offer 8 in the first temple and go ahead with 6. Double them and make them 12. Offer 8 again and go ahead with 4.
Double of 4 would be 8 that you would offer in the third temple.

Answer 1

assume that you start with 'x' flowers .after the first wash the no: of flowers become 2x.assume that you place 'y' flowers in the temple.the total no: of flowers become 2x-y.when you wash them in the second well they become 4x-2y,placing y flowers again you have,4x-3y flowers remaining,after washing in the third well you will have 8x-6y flowers,after placing y flowers you have 8x-7y flowers,which are ultimately equal to 0

8x-7y=0
8x=7y
least common multiple of 8 and 7 is 56.
therefore x=7
y=8
multiples of 7 and 8 can also take the values of x&y respectively.you can observe the following pattern
for three temples you require to take 7 flowers and place 8 flowers after doubling.
similarly you have to take 14 flowers for four temples and have to place 16 flowers after doubling.henceforth we can observe that
no: of flowers temples
7 3
14 4
..
.
.
.
. .
7(n-2) (n-2)
7n+12 n
therefore for n temples you need to take 7n+12 flowers and have to offer 8n+16 flowers to god.

Answer 2

Let n = number of temples (and wells)
then 2^n is the number of flowers to offer at each, and 2^n - 1 is the number of flowers to start with.

Answer 3

The way to solve this is to work backwards:

Let x = no. of flowers that you give each temple.

So, ((x/2 + x)/2 + x)/2 = 7x/8 = number of flowers at beginning

Since we're dealing with integers only, x can be any multiple of 8, and no. of flowers we start with corresponds to 7x/8.

So there are infinite solutions:

7,8
14,16
21,24
etc.