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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

bobbym wrote:

A toughie:

One bacterium is placed in a petri dish that has an infinite food supply and infinite space. Every fifteen minutes the bacterium either dies or splits in two with probability of 1/2. Now the two bacteria have the same property, each one either dies in 15 minutes or splits in two with probability of 1/2 etc. What is the chance that the colony dies out?

A says) How gross, besides math doesn't work in biology.

B says) Why on earth not? It's a tough problem but...

C says) The colony never dies out and I can prove it.

D says) If we could figure it, we would find that the colony is doomed.

E says) Wow! A is really smart.Pick one and prove he is right! You are disqualified if you pick A or E.

D the gravity would make it die

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi LQ;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

gravity would make it die, because space does not expand quick enough to pull the bacteriafood outwards.

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi LQ;

This is going to sound strange to you but to a bacterium, gravity is a feeble, undetectable force. Brownian motion, visible on them under a microscope is what they experience strongly.

And remember this is an a idealized problem, so the laws of physics can be left out.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

allright then. So it doesn't die of physical heat? that it burns up eventually? you have an infinite cooler?

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Ah hah, caught you there. Of course I do, look at the threads name. In here it is all cool.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

Eventually there would form diseases/viruses that killed all of the bacterias or that they evolved, eventually they wouldn't sustain. Questions on that?

PS. could we discuss some more about the oil and the hurricane?

*Last edited by LQ (2010-06-27 06:01:28)*

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Yes, if you want but you are in the the wrong thread for that. This thread is just for math questions.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Why did the vector cross the road?

It wanted to be normal.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi mathsyperson;

Yes, that is correct. Good work!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

ABC is a triangle (AB = AC) and apex angle of 20°, BC = AE. Find <AEC.

There are 6 known solutions to this, can you find a different one?

A says) 150°

B says) That's not right.

C says) 140°

D says) That's right!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**jimmyR****Member**- Registered: 2009-05-29
- Posts: 143

In post 125 you ask what is the next number in the sequence?

3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, __?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi Jimmy;

That is absolutely correct! Wunderbar!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Between 1700 and 2010 inclusive how many years have 365 days in them.

A says) 101

B says) 100

C says) 99

D says) 218

Who is right!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**jimmyR****Member**- Registered: 2009-05-29
- Posts: 143

Between 1700 and 2010 inclusive how many years have 365 days in them?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Hi jimmyR;

That is correct!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**jimmyR****Member**- Registered: 2009-05-29
- Posts: 143

That was very easy, how come no one got it?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

I cannot say. I thought there would be a couple of answers to that one. Probably no one saw it. Generally, I post in obscurity.

P.S. I corrected your bad spelling!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

B says "hey I found a neat proof that a square is the rectangle with the biggest area for a fixed perimeter. and it doesn't use any calculus. Instead it uses a little error analysis borrowed from numerical analysis.

If the rectangle is a square then the area is s*s = s^2, If it is a rectangle then it can represented as s + e and s - e. Sort of like a 5x5 square and a 7x3 rectangle, e would be 2 in that case. The area of that rectangle is (s + e)(s - e) = s^2 - e^2. Clearly s^2 is greater than s^2 - e^2, so we are done.

A says) Nonsense! If that is a proof I am Eisenstein!

B says) Sure it is a proof!

C says) Who is Eisenstein?

D says) I haven't disagreed with A since 1971 and I ain't starting now!

E says) Another crazy idea from B!

Who is right?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Here is another! The fun just keeps on!

Is it possible to tell whether the random number generator that excel uses is a linear congruential one? Can that be done mathematically with just some output from the generator to study?

A says) No way! Random numbers can't be understood or analyzed.

B says) Sure, you can even tell what the parameters are as long as it is a linear congruential generator.

C says) There might be a way but I don't remember it. I think it can be done with vectors.

D says) I sure don't agree. How can you tell all that from just a few outputted numbers. I think A is right.

Who is right? Prove your assertion, one way or the other.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

Someone is given this problem to solve:

Find the equation of the tangent at the point (a,b) to the curve xy = c2.

He solves it like this.

You must solve for g in:

He merrily substitutes (a,b) for x , y and gets.

solving for g:

g is the y intercept.

The equation of the tangent is:

He/she is happy they have solved for the tangent to c^2 = xy for any a,b,c.

B says) That is beautiful, that is exactly what I would have done.

A says) For the first time I agree with B that is nice.

C says) Agreed.

D says) Man, I wish I could do that.

Do you agree with our panel of experts?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

The two worm problem.

Two worms investigate an apple. Worm A says,"I can eat that apple at the rate of 2% of the remaining apple on each bite." Worm B says,"I can do better than that ( meaning his rate is higher than 2% of the remaining apple on each bite ), let's eat it." Worm A takes a bite and then worm B takes a bite. They proceed taking alternating bites.

After worm B has taken the 128th bite. They stop to rest. Worm A notices that exactly 1 / 7 of the apple remains.

Worm B says,"Are you sure it is 1 / 7, doesn't that prove I have a higher rate than you." Worm A says,"no way pal, I have the higher rate."

Which worm is right?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

A and B continue the argument from

http://www.mathisfunforum.com/viewtopic … =12832&p=6

post #109

B has been taking the (1,2) and A the (1,1) for two days and B is killing A.

A says) You are cheating me!

B says) Nope, (1,2) is expected to come up in less throws than (1,1) in our game.

A says) Bull! My (1,1) should come up before your 1,2. I have the advantage.

B says) The expected number for your (1,1) is 42 rolls, while mine is 36 rolls. Plain math man!

A says) I have the advantage, I don't know about this expectatiton of yours but here is why my (1,1) should take less rolls than yours!

A's simple explanation:

Think of the throws as a bunch of numbers from 1 to 6, with 1's sprinkled around among them. Look at any 1. I can have a winner with a 1 in front or a 1 in back. You can only have a winner with a 2 in back. I have the edge.

B knows that is wrong. He has an empirical experiment ( they have been playing for days and A is busted ). He knows the expected number is 42 for the (1,1) and 36 for the (1,2) to show up. But he is unable to batter down A's simplistic analysis.

What is wrong with A's analysis...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,233

A simple one!

Prove that ln(x) < x - 1 when x > 1. You are not allowed to use convexity or concavity, increasing functions or any calculus at all.

A says) Can't be done, not without my beloved concavity.

B says) Hmmm, looks tough.

C says) I can't do it either, you need calculus.

D says) I got it!

Can you do as well as D?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 120

Well,

Here's my attempt at a proof...

I'm happy to be back on mathisfun!

*Last edited by Fruityloop (2010-10-15 15:01:09)*

The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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