Bafflers?

bobbym · 2012-03-04 02:14:05

You were there when I answered John Franklin's question. It was so easy he picked up on it right away. Do you need more than that?

anonimnystefy · 2012-03-04 02:24:49

Ok, I get that one, but look at this problem;

You have ten pigeons and you have to arrange them into three cages so that in every cage the is at least 1 pigeon.You can assume the pigeons to be all the same.the same goes for the cages.In how many ways can you arrange the pigeons into cages under the given conditions?

bobbym · 2012-03-04 02:33:05

Hi;

There are 36 ways.

anonimnystefy · 2012-03-04 02:35:20

How did you get that?

bobbym · 2012-03-04 02:38:49

You are trying to solve the diophantine equation

a+b+c=10 with 0<a,b,c<11

anonimnystefy · 2012-03-04 02:42:13

That's pretty much it.But how do you arrive at the answer with GF's?

bobbym · 2012-03-04 02:46:08

Now check the coefficient of x^10.

anonimnystefy · 2012-03-04 03:04:52

But what about the condition that there of at least one pigeon on each cage?

bobbym · 2012-03-04 03:06:20

Hi;

Took a while to edit post #82. The polynomial takes that into account automatically.

anonimnystefy · 2012-03-04 03:11:47

So we just take out the 1.

bobbym · 2012-03-04 03:14:38

Yes. The 1 represents x^0. There is no 0 choice because there must be at least one pigeon per box.

anonimnystefy · 2012-03-04 20:42:19

Hi bobbym

Then I'm clear on that part.Just have one question.For the x^10 we use asymptotic analysis on the forum right? But, when I do these problems when I'm not allowed to use Wolfram and that stuff, how do I then get the Laurent series?

bobbym · 2012-03-04 23:07:57

You do not need a Laurent series here. There are ways that help you get the coefficients we need. But they are rather limited. There are limits to what can be done by hand.

anonimnystefy · 2012-03-04 23:50:45

And what's that way? And what if I wanted the answer in binomial form?

Btw, do you know what Eurovision is?

bobbym · 2012-03-04 23:57:27

Hi;

The other method would be to use series methods on

it does not look very promising though.

I have not heard of Eurovision.

anonimnystefy · 2012-03-05 00:10:40

Ok, but if I wanted it in the binomial form?

bobbym · 2012-03-05 00:12:32

Then you would have to solve the diophantine equation using the formula.

anonimnystefy · 2012-03-05 00:23:34

But is there a way to get it directly out of the GF?

bobbym · 2012-03-05 00:25:37

In this case you could play spot the pattern with the generating function. Other methods do not look promising.

anonimnystefy · 2012-03-05 00:36:20

Ok, then.When can we expect more problems?

bobbym · 2012-03-05 00:39:12

As soon as I get back here.

anonimnystefy · 2012-03-05 00:54:24

Back where?

bobbym · 2012-03-05 03:25:15

Back in the forum. I have some work to do.

anonimnystefy · 2012-03-05 07:17:03

So where's the problem?

bobbym · 2012-03-05 08:58:33

Baffler #2

A ship is sailing on a course from the origin. It follows the path y= 3.14 x. It has a speed of 1 / 3 units per second. A submarine is located at (5,0). The sub knows the ship is oblivious to its existence. The sub would like to torpedo the warship. Torpedoes travel at 1 / 2 units per second and travel in straight lines. The sub commander's hobby is mathematics. He fires and sinks the ship! What is the equation of the torpedoes flight?

A says) Too easy, here is the answer!

B says) I am astounded, you got the right answer!

C says) A is my hero.

D says) Hip hip hooray!

E says) Even a blind squirrel finds an acorn now and then.

B says) How true.

Find that equation. If A got it then so should you!

Math Is Fun Forum

#76 2012-03-04 02:14:05

Re: Bafflers?

#77 2012-03-04 02:24:49

Re: Bafflers?

#78 2012-03-04 02:33:05

Re: Bafflers?

#79 2012-03-04 02:35:20

Re: Bafflers?

#80 2012-03-04 02:38:49

Re: Bafflers?

#81 2012-03-04 02:42:13

Re: Bafflers?

#82 2012-03-04 02:46:08

Re: Bafflers?

#83 2012-03-04 03:04:52

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#84 2012-03-04 03:06:20

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#85 2012-03-04 03:11:47

Re: Bafflers?

#86 2012-03-04 03:14:38

Re: Bafflers?

#87 2012-03-04 20:42:19

Re: Bafflers?

#88 2012-03-04 23:07:57

Re: Bafflers?

#89 2012-03-04 23:50:45

Re: Bafflers?

#90 2012-03-04 23:57:27

Re: Bafflers?

#91 2012-03-05 00:10:40

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#92 2012-03-05 00:12:32

Re: Bafflers?

#93 2012-03-05 00:23:34

Re: Bafflers?

#94 2012-03-05 00:25:37

Re: Bafflers?

#95 2012-03-05 00:36:20

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#96 2012-03-05 00:39:12

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#97 2012-03-05 00:54:24

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#98 2012-03-05 03:25:15

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#99 2012-03-05 07:17:03

Re: Bafflers?

#100 2012-03-05 08:58:33

Re: Bafflers?

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