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        riddles >> easy >> Two people went fishing
        
(Message started by: Lewis Temple on Dec 9^th, 2004, 6:00pm)

Title: Two people went fishing
Post by Lewis Temple on Dec 9^th, 2004, 6:00pm

Two people went fishing one day, they fished hard all day and had a good day because they both caught some fish. When they returned to shore and started cleaning the fish they discovered that if person A gave person B one of his fish they would have the same number of fish, but if person B gave person A one of his fish A would have twice as many as B.

How many fish did they catch.

Title: Re: Two people went fishing
Post by THUDandBLUNDER on Dec 9^th, 2004, 8:36pm

[hide]Let person A have x fish.
Let person B have y fish.

Then
x - 1 = y + 1
x + 1 = 2(y - 1)

Giving x = 7, y = 5

More generally (I remember working this out when I was at college),
Person A: If you give me a of your fish, I will have b times as many as you.
Person B: If you give me c of your fish, I will have d times as many as you.

This has the solution
x = c + [(a + c)(b + 1) / (bd - 1)]
y = a + [(a + c)(d + 1) / (bd - 1)]
provided
bd - 1 divides (a + c)(b + 1)
AND
bd - 1 divides (a + c)(d + 1)
[/hide]

Title: Re: Two people went fishing
Post by Lewis Temple on Dec 9^th, 2004, 8:58pm

yea, but could you hide it so others might enjoy?

Title: Re: Two people went fishing
Post by THUDandBLUNDER on Dec 9^th, 2004, 9:05pm

on 12/09/04 at 20:58:58, Lewis Temple wrote:

yea, but could you hide it so others might enjoy?

Done.
Yes, I'm sure they'll rack their brains over this one!

Title: Re: Two people went fishing
Post by Lewis Temple on Dec 9^th, 2004, 11:06pm

Thank you, and i am sure some will enjy racking their brains over it, not all of us are as intellectual as you are.

Thank you again!

Title: Re: Two people went fishing
Post by THUDandBLUNDER on Dec 10^th, 2004, 7:49pm

on 12/09/04 at 23:06:38, Lewis Temple wrote:

not all of us are as intellectual as you are.

Well, I don't know whether to be pleased, disappointed, embarrassed, or offended. :D
But I think you will agree that the puzzle is almost as easy as it is old.
(I believe it dates back to Euclid, about 300 BC.)

Title: Re: Two people went fishing
Post by Lewis Temple on Dec 10^th, 2004, 8:12pm

I in no way meant that remark to be derogatory, I have the utmost respect for you and your train of thought. I am fascinated at how people come to conclusions to answers, for example you did the math equations and figured it out very methodically where as I did it with some little metal parts and another person. ;^)

Title: Re: Two people went fishing
Post by THUDandBLUNDER on Dec 11^th, 2004, 7:16pm

Quote:

where as I did it with some little metal parts and another person. ;^)

An excellent idea. :)
I assumed that you had invited a friend to go fishing.