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The Flowers

Puzzle:

In a small town, there are three temples in a row and a well in front of each temple. A pilgrim came to the town with certain number of flowers.

Before entering the first temple, he washed all the flowers he had with the water of well. To his surprise, flowers doubled. He offered few flowers to the God in the first temple and moved to the second temple. Here also, before entering the temple he washed the remaining flowers with the water of well. And again his flowers doubled. He offered few flowers to the God in second temple and moved to the third temple. Here also, his flowers doubled after washing them with water. He offered few flowers to the God in third temple.

There were no flowers left when pilgrim came out of third temple and he offered same number of flowers to the God in all three temples. What is the minimum number of flowers the pilgrim had initially? How many flower did he offer to each God?

For Solution SCROLL DOWN...



































Solution:

The pilgrim had 7 flowers, initially and he offered 8 flowers to each God.

Assume that the pilgrim had X flowers initially and he offered Y flowers to each God. From the data in puzzle, there are (8X - 7Y) flowers when the pilgrim came out of the third temple. But it is given that there were no flowers left when he came out of third temple. It means that
(8X - 7Y) = 0 or 8X = 7Y
The minimum values of X and Y are 7 and 8 respectively to satisfy above equation. Hence, the pilgrim had 7 flowers and he offered 8 flowers to each God.

In general, the pilgrim had 7N flowers initially and he offered 8N flowers to each God, where N = 1, 2, 3, 4,

82 comments:

Aravinda Raghuram said...

Minimum number of flowers with which the piligrim enters the temple = 7

Flowers offered at each temple = 8

let x be the number of flowers
let y be the number of flowers offered at each temple

At temple 1:
Let z be the number of flowers left
thus 2x-y=z

At temple 2:
Number of flowers the piligrim intially has after offering at temple 1= z
Let p be the number of flowers left
thus 2z-y=p

At temple 3:
Number of flowers the piligrim intially has after offering at temple 2= p
After offering at temple 3 he dowesn't have any flowers
thus 2p-y=0
=>p=y/2
thus by solving the above 2 equations we get x=7y/8

As number of flowers should be a digit..y should be a multiple of 8
minimum value for y=8
thus x=7

so Intially the piligrim has 7 flowers and offered 8 flowers at each temple

Anonymous said...

He had 7 flowers, offered 8 at each temple

Anonymous said...

compared to Chavali's answer it is teadious and not suitable for long sequence
Anyway let x be initial no. of flowers and y be the flowers offered at each temple.
Then sequence goes as
Initial flowers = x
after crossing first well = 2x
offering @ first temple = y
remaining = 2x-y
after crossing second well = 4x -2y
offering @second temple = y
remaining = 4x-3y
after crossing third well = 8x-6y
offering @ third temple = y
remaining = 8x-7y which is zero.
Therefore, 8x-7y=0;
8x=7y, and least possible solution for this is x=7 & y=8;

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Balaji said...
This comment has been removed by the author.
Patil's All in One said...

I designed a easier solution. more generalised form.

the answer is

2^n-1 no of flowers intially he was carrying.

2^n no of flowers he kept at first temple.

where n is no of temples.
and 2^n represents 2 power n.

Patil's All in One said...

If u think my formula is helpful please post ur comments and follow my blog so that i get to know was that formula useful to anyone...

Anonymous said...

Patil, what you say is right but I would think a prove is in order. I thought of one.

Lemma 1: For n is the amount of temples visited before we end op with E_n flowers (with E_n = 0 for the final temple), the following holds: 2^n * S - (2^n - 1)I = E_n, where S is the amount of flowers at the start and I is the amount of flowers offered.

Proof by induction
Base case: For 1 temple visited, we double our S and then offer i flowers to the gods. So we have 2S - I = E_1, alternatively, 2^1 * S - (2^1 - 1)I = E_1, so the base case holds for n = 1.
Induction Hypothesis: 2^n * S - (2^n - 1)I = E_n
Induction:
2(E_n) - I = E_n+1

2(2^n * S - (2^n - 1)I) - I = E_n+1.

2^n+1 * S - (2^n+1 - 2)I - I = E_n+1.

2^n+1 * S - (2^n+1 - 1)I = E_n+1.

The lemma has been proven.

We know that if we visit n temples, with S starting flowers and I offered flowers per temple, we have E_n = 2^n * S - (2^n - 1)I (lemma 1). Also we know that E_n = 0 since we end up with 0 flowers at the end.

So we know:

2^n * S - (2^n - 1)I = 0
2^n * S = (2^n - 1)I

Since the coefficients of S and I are one apart, they are per definition co-prime. So except for 1 they have no common divisor. We know a possible integer solution for the equation is S = 2^n - 1 and I = 2^n. Since the numbers are co-prime, we can not S and I by any number (other than the identity element 1) without making the solution non-integer. So S = 2^n - 1 and I = 2^n is the smallest integer solution for the problem.

QED
(I do not know if the part about proving it's the smallest is rigorous enough, anyone know a better way of showing it's the smallest integer solution?)

yogesh mundkar said...

spouse> Initially He has X flower
> flower offered is Y
In 1st Temple
X become 2x out of these He offer Y then >Total flower remain(2X-Y)

In second Temple
(2X-Y) became (4X-2Y)out of these He offer Y Then> total flower Remain(4X-3Y)

In 3rd temple
(4x-3Y) became (8x-6Y) out of these he offer Y flower Then > total flower Remain (8X-7Y)

But..........
AT End Zero flower remain
Their-four (8X-7Y)=0
8X=7y
X=7 and Y=8

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Unknown said...

Wat ll b d solution if its 4 temple

Unknown said...

Wat ll b d solution if its 4 temple

Unknown said...

I think there will be no answer....😂😂

Unknown said...

I actually came up with this solution while I was about to fall asleep last night.

The pilgrim starts with 7 flowers and leaves 8 at each temple.

At the first temple his flowers double to 14. He leaves 8 and has 6 remaining flowers.

At the second temple his flowers double to 12. He leaves 8 and has 4 remaining flowers.

At the third and final temple his flowers double to 8. He leaves 8 and has 0 remaining flowers.

Then he goes on to complete the next logic puzzle!

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marigouda said...

let he offers 'X' flowers in all temple.
1) during third wash he has X/2 flwrs
(while entering he has X+X/2=3X/2)

2). during 2nd wash he has 3X/4 flwrs
(while entering he has X+3X/4= 7X/4)

3). @ 1st wash he has 7X/8 flwrs

he can offer any number of flwrs but that should be multiple of 8.

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laura said...


am so happy to share this great testimony and say a big Thank to Dr okeke for what he have done for me! with his spell am laura from USA my family is back My husband has come back home with the help of okeke and now my husband has stopped to fill the divorce papers after i contacted Dr okeke to help me stop the divorce with my husband and now things are going much better now. As Dr okeke said, all the process concerning the divorce have been cancelled and the evil woman that cause the problem in my marriage has be sent away by my husband and we are now happy together. i said it better for me to share this good news and good work of Dr okeke with everyone here I will advice if you are passing any problem in your marriage or relationship reach Dr okeke his the solution to your problem and predicament Thank you okeke for your help reach him on email at (writelovespell@gmail.com) or chat him on WhatsApp on (+2348140443360) he can also help you with the following problem
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Am here to say a big thank you to Dr Sam for his great powerful love spell and his great spirits for saving my relationship. No one would have believe that I and my ex will ever come back together again lovers. But this great spell caster united us in just 48 hours. Dr Sam is truly a real and honest online spell caster. Contact him now on: okokakspellhome@gmail.com or whatsApp him +2349060421250 and he will help you solve all your problem

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Hello my name is Belinda i want to share my amazing experience with the greatest spell caster Dr irekenagba. my husband was cheating on me and when i found out we had a fight which lead to him filling for a divorce i cried and fell sick when i was searching about love quotes online i saw people talking about him and his great work whose case was similar to mine they left his contact info i contacted him and he told me not to worry that after 24hrs he will cancel the divorce and be back to me after i did everything he asked me to do to my greatest surprise the next day evening it was my husband he knelt down begging me to accept him back,thank you once again Dr irekenagba you are indeed a blessing to me he can also help you contact him on........
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Hello my name is Martha Keith, Am here to testify of a great and powerful spell caster named Dr Sunny, I was so confused and devastated when my Husband left me for another woman. I needed him back desperately because I loved him so much. So I contacted this great love spell caster for help. He helped me cast a return love spell on my husband and just within 40hours my husband came back to me begging for my forgiveness. Dr Sunny released him to know how much I loved and wanted him back. And He also opened his eyes to picture how much love we have shared together. As I am writing this testimony right now I am the happiest woman on earth. I want to recommend this great spell caster to anyone that truly needs an urgent solution to a love break up Email him at {solutioncentre911@gmail.com}   or via his whats-app: +2349056393169 his Also specialize in the following spell below,
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