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Broken Puzzle/Math/question I would like the answer to.

BrIONwoshMunky

EVERYBODY LOVE EVERYBODY!
Staff
9,588
1,279
387
#1
Ok, say I have 6 inputs/switches. Either on or off.

A
B
C
D
E
F

And I want to turn on a light. To get it to turn on all the way, I have to turn on all 6 inputs/switches.

A+B+C+D+E+F= 1

But, if i want the light, half on, I can turn on F.

F = 1/2

A+B+C+D+E=1/2

what ratios/fractions/whatever can A,B,C,D, and E equal, so that the sum of them equals 1/2 and A<B<C<D<E

I know this is somehow a simple binary problem, but I just can't figure the math out.

I think it's like if in binary, you had 100, you have 2... but if you had 000001, what is that?

Bah, it should be simple.

EDIT: I'm going to paraprhase what I want to do.

A+B=C
A+B+C=D
A+B+C+D=E
A+B+C+D+E=F
A+B+C+D+E+F=1
F=1/2
 

Tostig

Paradoxasaur
8,339
33
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#2
Actually, in Binary, 10=2.

does E have to be less than F? Can there be negatives? Any other rules?
 

Woodreaux

Original Dicksman
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#3
A+B+C+D+E+F=1/2
use recurssion:
let A = 1/4 --> B+C+D+E+F = 1/4
let B = 1/8 --> C+D+E+F=1/8
let C = 1/16 --> D+E+F=1/16
let D = 1/32 --> E+F = 1/32
let E = 1/64 --> F = 1/64
Substituting these values in you get:
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64 =
16/64 + 8/64 + 4/64 + 2/64 + 2/64 = 32/64 = 1/2
 

Slacker

Postaholic
3,735
139
127
#4
Woodreaux said:
A+B+C+D+E+F=1/2
use recurssion:
let A = 1/4 --> B+C+D+E+F = 1/4
let B = 1/8 --> C+D+E+F=1/8
let C = 1/16 --> D+E+F=1/16
let D = 1/32 --> E+F = 1/32
let E = 1/64 --> F = 1/64
Substituting these values in you get:
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64 =
16/64 + 8/64 + 4/64 + 2/64 + 2/64 = 32/64 = 1/2
I had the same thing but different wording and I thought I was wrong.
 

Tostig

Paradoxasaur
8,339
33
142
#5
I figured it out over break in percentages

F=1/2
F=50%
A+B+C+D+E=50%
A=1%
B=5%
C=10%
D=15%
E=19%

1+5+10+15+19=50
 

BrIONwoshMunky

EVERYBODY LOVE EVERYBODY!
Staff
9,588
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387
#6
Awesome. Ha ha.

That was too simple... Stupid me.
 

Tostig

Paradoxasaur
8,339
33
142
#7
Woodreaux said:
A+B+C+D+E+F=1/2
use recurssion:
let A = 1/4 --> B+C+D+E+F = 1/4
let B = 1/8 --> C+D+E+F=1/8
let C = 1/16 --> D+E+F=1/16
let D = 1/32 --> E+F = 1/32
let E = 1/64 --> F = 1/64
Substituting these values in you get:
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64 =
16/64 + 8/64 + 4/64 + 2/64 + 2/64 = 32/64 = 1/2
There's a problem with this one...

You have F=1/64 when the problem states that F=1/2. A+B+C+D+E=F AND A<B<C<D<E or A>B>C>D>E (either way you get the same results).
So if you do A=1/4, b=1/8, C=1/16,D=1/32 , D=1/64you get:
A=16/64, B=8/64, C=4/64, D=2/64, E=1/64
A+B+C+D+E=31/64, 1/64 shy of 1/2. So the whole solution with F would = 63/64
 

Woodreaux

Original Dicksman
2,429
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#8
you're right. I didn't read the inequality constraint. Tostig's percentage solution is good idea, and simple too.
 
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#9
Tostig said:
I figured it out over break in percentages

F=1/2
F=50%
A+B+C+D+E=50%
A=1%
B=5%
C=10%
D=15%
E=19%

1+5+10+15+19=50
BrIONwoshMunky said:
EDIT: I'm going to paraprhase what I want to do.

A+B=C
A+B+C=D
A+B+C+D=E
A+B+C+D+E=F
A+B+C+D+E+F=1
F=1/2
your A + B = 6%, not C (10%) as the rules require.
 

Tostig

Paradoxasaur
8,339
33
142
#10
The rules, as originally posted, don't require A+B=C. Only that A+B+C+D+E=F and A>B>C>D>E or A<B<C<D<E
 

Stardust

Being naked just feels so a-peeling
6,696
2,615
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#11
sorry I just have to say this...
YAIKS! :eek: I can't even start to understand that..I'm waay to stupid.. :happysad:
 

Tostig

Paradoxasaur
8,339
33
142
#12
not getting math doesn't make you stupid. You're just wired differently.

I didn't "get" art in school. I appreciate good art, but i can't draw to save my life.
 
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#13
32 16 8 4 2 1
A=1/48 0 0 0 0 0 1
B=2/48 0 0 0 0 1 0
C=3/48 0 0 0 0 1 1
D=6/48 0 0 0 1 1 0
E=12/48 0 0 1 1 0 0
F=24/48 0 1 1 0 0 0
1=48/48 1 1 0 0 0 0

I think this is right
 

Base

it's a motherfucker
1,833
1
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#14
zues696 said:
32 16 8 4 2 1
A=1/48 0 0 0 0 0 1
B=2/48 0 0 0 0 1 0
C=3/48 0 0 0 0 1 1
D=6/48 0 0 0 1 1 0
E=12/48 0 0 1 1 0 0
F=24/48 0 1 1 0 0 0
1=48/48 1 1 0 0 0 0

I think this is right
just what i thought :happysad:
 

CopyLifted

Funnier than a 5th grader
4,790
78
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#15
I'm going to be a linsky too.

I knew the answer but I didn't have a clue what you were talking about so I thought I'd agree with somebody. :happysad: