Puzzle - Brain-box help needed!

[chim_knee]

Someone has asked me to help them solve this... and I wondered if I can rely on the PH collective to make me look great!

One caveat... the puzzle may have some crucial piece of information missing as the person who sent it isn't renowed for their attention to detail!

This is the puzzle:

You have a certain number of flowers to take to a church.
When you reach the entrance of church 1 the number of flowers that you started with doubles.
You lay a certain number of flowers and move on to church 2.
When you arrive at church 2 the number of flowers that you have doubles again.
You lay the same amount of flowers as before and then leave for church 3.
When you arrive at church 3 the same thing happens again, your flowers double and you lay the same amount but when you leave the church you have no flowers left.
How many flowers did you have to start with?


Now, I have had a stab at it and in best school-boy mode have "shown my working out"... can anyone tell me where I am wrong and (probably) why I am so wrong!!

You have a certain number of flowers to take to a church. No of flowers = x
When you reach the entrance of church 1 the number of flowers that you started with doubles. 2x
You lay a certain number of flowers and move on to church 2. Leave "y" flowers => 2x-y
When you arrive at church 2 the number of flowers that you have doubles again. 2(2x-y)
You lay the same amount of flowers as before and then leave for church 3. 2(2x-y)-y
When you arrive at church 3 the same thing happens again, your flowers double (2(2(2x-y)-y))and you lay the same amount but when you leave the church you have no flowers left.

=> 2(2(2x-y)-y)-y = 0
=> 2((4x-2y)-y)-y = 0
=> 2(4x-3y)-y = 0
=> 8x-6y-y = 0
=> 8x-7y = 0

How many flowers did you have to start with?

And now I'm stuck!

TIA!
Phil

[mybrainhurts]

How do you get flowers to breed like that....?

[pdV6]

I've got as far as you, i.e x = 7/8 y

Therefore, without more information, there's a whole range of values for x, following the 7x table.

e.g. start with 7 flowers
at C1, you get an extra 7 and leave 8, 6 remain
at C2, you get an extra 6 and leave 8, 4 remain
at C3, you get an extra 4 and leave 8, none remain

Same would be true for 14 flowers initially, leaving 16 at each church...

[thub]

8x-7y=0
8x=7y
x=7y/8

lowest whole numbers
x=7
y=8

As pdV6 points out, any multiple of 7 & 8 would work.

>> Edited by thub on Thursday 3rd February 11:24

>> Edited by thub on Thursday 3rd February 11:25

[chim_knee]

pdV6, thub: Ta! I think the answer will be 7 as it is indeed the lowest whole number. I can't believe I missed off the final step but hey-ho!

Thanks again - off to bask in the glory now...

[Coxy the Bear]

Start with 7 and lay 8 each time. This wasn't difficult was it?

[chim_knee]

Coxy the Bear said:

Start with 7 and lay 8 each time. This wasn't difficult was it?

No mate, hence the answer having been posted ages ago.