Good luck on this puzzle...

I

Izuk

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Joined
Sep 12, 2006
Messages
4
Not sure where to post this. It's not for a class and I'm not sure what math is involved.

a(2b+c) = 30
d+a+c = 26
e(b+f)-(e^2+3e) = 91
g(d)/(d+2a) = 12

Solve for a, b, c, d, e, f, g
This has had me stumped for months.
I don't even know where to begin.
 
Your going to have to define what you mean by "stumped".
You will have to suggest why you are doing this.
Generally, having seven variables and only four relationships is an insufficient description for a unique solution.

Here is one solution:

a = -6
b = -9.5
c = 14
d = 18
e = 10
f = 25.6
g = 4

Here is one with everything positive:

a = 1.5
b = 2.25
c = 15.5
d = 9
e = 5
f = 17.95
g = 16

So, what is it that you seek?
 
It's for a hide and seek game.

I was unable to come up with any solution at all for those variables (which is what I meant by "stumped"). By nature, I'd imagine that every variable needs to equal a positive whole number, but I'm not totally sure.

Is there a program that's good for solving this type of problem or did you sit down and figure this out with pencil/paper or Excel, etcetera?

Thanks for your help. :)
 
Izuk said:
Is there a program that's good for solving this type of problem or did you sit down and figure this out with pencil/paper or Excel, etcetera?
Click to expand...
There are seven variables and only four equations. It doesn't matter how you approach this; it is not mathematically possible to obtain a unique solution. Sorry.

Eliz.
 
I don't need a unique solution. Just some solutions with positive whole numbers if possible.

I know this isn't a great puzzle or anything, but it is important to me.

Thanks for the input, y'all. :)
 
Here's an integer > 0 solution: a,b,c,d,e,f,g = 1,4,22,3,7,19,20

As far as a program goes, easy enough; here's quickie in Basic:

Loop a from 1 to k
Loop b from 1 to k
c = 30 - 2*a*b : if c < 1 then next a
c = c / a : if c <> integer then next b
d = 26 - a - c : if d < 1 then next b
Loop e from 1 to k
f = 91 + e^2 + 3*e - b*e : if f < 1 then next e
f = f / e : if f <> integer then next e
g = (24*a + 12*d) / d : if g <> integer then next e
print a,b,c,d,e,f
endloops
 
Thanks, Denis.

That code looks like it will work great and I'll play with those numbers and see if they mesh into the game like I need them to.

Thanks to everyone else who's helped out, too. It's good to see an active forum that doesn't hesitate to try to lend a helping hand!
 
Just curious? Geocaching?

Is your problem for a Unknown (Mystery) Cache?
When you mentioned a hide and seek game I figured it was Geocaching.
I've posted here just last night looking for help on a cache problem.
Any way just curious, if it's not Geocaching what game is it?
 
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