Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#26 2011-08-07 21:39:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Hi;

I was doing something like that up to post #9, when I saw his answer it did not fit my eqautions because his answer uses only 3 on the left. Anyway is this what you are solving:


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#27 2011-08-07 21:48:28

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Balancing Act

Hi bobbym,

I see 4 weights on each side, I don't understand how you see only 3 weights on the left.

Yes, that's my equation, along with the condition that they are distinct.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#28 2011-08-07 21:57:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Hi gAr;

It was the only way I thought to get his book solution in post #8.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#29 2011-08-07 22:07:51

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Balancing Act

Hi,

But you said you got 184 solutions?

And in #14 you wrote

3*9 + 2*5 + 2*8 = 1*7 + 3* 2 + 1*4 + 3* 6 + 6 * 3

It should be

3*9 + 2*5 + 1*12 = 1*7 + 3*2 + 4*9


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#30 2011-08-07 22:14:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Hi;

You have totally different idea than I had. Yours works. One question for the two on the bottom, I see 1* 12, how do you get 4 * 9?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#31 2011-08-07 22:18:17

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Balancing Act

hi all,

Only just got to this.  I think the rule

A weight that is placed two sections away from the middle will become twice as heavy as a weight that is placed one section away.

is just the 'law of moments'.  I'm with gAr on this one, and I agree with both answers. (#12)

bobbym: Post another of your solutions please and I'll check it again the law.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#32 2011-08-07 22:21:07

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Balancing Act

Hi,

That's not my idea, that's how torques are to be calculated !

The masses of the sub balances are added.
So in 1*12, 1 is the distance from the fulcrum and 12 is the weight in the sub balance: 8+4
Similarly the 4*9 : 4 is the distance from fulcrum, 9 is the weight 6+3

Hi Bob,

Just saw your post.
Yes, the "law of moments". I keep on forgetting the names!

Last edited by gAr (2011-08-07 22:23:16)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#33 2011-08-07 22:23:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Hi;

None of my solutions are correct. I think I got messed up. One more question though, when I solve gAr's equations I get:

This does not coincide with gAr's post #12.

Post #26 is what I used.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#34 2011-08-07 22:25:14

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Balancing Act

Hi bobbym,

Is it displayed in the right order? a,b,c... ?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#35 2011-08-07 22:30:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Hi gAr;

Yes, what did I do wrong?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#36 2011-08-07 22:32:15

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Balancing Act

hi bobbym

see picture

edit

3d+2b+3a=e+2f+12h

I think you meant 3f


Bob

View Image: balance.GIF

Last edited by bob bundy (2011-08-07 22:40:38)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#37 2011-08-07 22:40:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Hi bob;

Thanks for the drawing, I think I got it. It looks too simple to make a mistake on but...

Hi gAr;

I still can not genenrate your answers.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#38 2011-08-07 22:41:11

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Balancing Act

see above edited post

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#39 2011-08-07 22:44:37

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Balancing Act

Hi all,

2*d = c
g = 2*h
(c+d)+2*b+3*a = e + 3*f + 4*(g+h)

Using first 2 equations, 3rd one is
3*d + 2*b + 3*a = e + 2*f + 12*h

Yes, that's 3f in the last one, sorry about that!
Now you would get it, bobbym.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#40 2011-08-07 22:45:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

Oh no! Yep, that is it. Yet another stupid blunder!

Thanks bob and gAr, I finally got it!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#41 2011-08-07 22:47:22

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Balancing Act

Hi bobbym,

Glad that you got it.
You're welcome!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#42 2011-08-07 22:47:49

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Balancing Act

"Glad to be of service"  ...Hitch Hikers Guide to the Galaxy

smile

Bob

Last edited by bob bundy (2011-08-07 22:48:05)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#43 2011-08-07 22:53:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,162

Re: Balancing Act

They say it is better medicine to get something wrong and learn then to get 10 problems right.

My brother says I am overdosing!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

Board footer

Powered by FluxBB