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

I don't know if it was appropriate to say QED in that, but it's just really cool to say. ^_^

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

mathsyperson, you are correct!

Character is who you are when no one is looking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

By mathimatical law, you can only say QED when you start out with "Pf" or "Proof". But we'll let you go with a warning this time.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Problem # k + 97

Two men set out at the same time to walk towards

each other from points A and B, 72 km apart. The first man

walks at the constant rate of 4 km/hr. The second man walks

1 km the first hour, 2 km the second hour, 3 km the third hour

and so on. When will the two men meet?

Character is who you are when no one is looking.

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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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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,585

On k + 89, I meant to multiply by 3, but then I still would be wrong.

I wish there was a theorum to get the number that is close to this 3.

I'll have to work on that. The 3 multiplier would be like having 4 + 4 + 4 in the numerator.

I know it is wrong, but I feel the need to research this further.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,585

On k + 89, I was below with this 3 times correction still by factor of 1.062801932.

So with the new correction factor, it's kind of dumb, but, you'll laugh, but...

percentage that it was from machine B knowing first that the piece is

defective = 35% ((4 x 3)/(5 + 4 + 2)) * correction factor, where correction factor = (5 + 4 + 2)/(3*(.35 x 4 + .25 x 5 + .40 x 2))

**igloo** **myrtilles** **fourmis**

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

*Last edited by irspow (2006-02-20 16:00:28)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Solution to Problem # k + 97

After 8 hours, the first man has walked (8x4) kilometers, i.e. 32 kilometers.

After 8 hours, the second man has walked (1+2+3+4+5+6+7+8) kilometers, i.e. 36 kilometers. In the ninth hour, the first man is walking at 4 km/hr and the second is walking at 9 km/hr. Let them meet after time t hours.

Hence, 4t+9t=4, 13t=4, t=4/13 hours = 18.46 minutes approximately.

Hence, they would meet after 8 hours and 18.46 minutes approximately.

mathsyperson is correct

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Problem # k + 98

A and B are two stations 300 km apart. Two trains T1

and T2 start from A and B respectively, towards each other at

the same time. T1 reaches B nine hours and T2 reaches A four

hours after they meet. Find the difference between the speeds

of T1 and T2.

Character is who you are when no one is looking.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

lol. You love this instantaneous velocity. I stand by my k+97 solution(s). There was nothing in the question that required the solution agreed upon. Distance travelled does not prove constant velocity during a time period. I have yet to see an instance of infinite acceleration either. My equations describe the motion of both people as correctly as your assumptions.

I am not trying to dispute your solution, just pointing out that the wording of a problem is just as vitally important as the mathematics that lead to a solution. Your solution **and** mine are equally valid given the way in which it was worded. More details would be needed to invalidate either one.

My answers are more correct though! Just kidding. Why quibble over less than 30 seconds?

*Last edited by irspow (2006-02-21 03:42:33)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

I concede you're correct too, irspow! The time given to solve the problem was about a minute! I thought the best way to do that was the way I solved

Character is who you are when no one is looking.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

Thanks for the concession. lol. Interesting how **both** are correct and yet different with a problem stated as such, no?

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Problem # k + 99

If y + 1/z = 1 and x + 1/y = 1, what is the value of xyz?

Character is who you are when no one is looking.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I love that kind of problems.

IPBLE: Increasing Performance By Lowering Expectations.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Character is who you are when no one is looking.

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

You're right, irspow, it would be more natural to model the man as having a constant acceleration like that, but ganesh did say that the men were moving towards each other, so the second part of your k+97 solution was not needed.

Why did the vector cross the road?

It wanted to be normal.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

I agree mathsyperson. I nit-pick too much sometimes. I wasn't trying to imply anything other than the **real** problems I was having with the solution and nothing more. I will admit it is a little bit of a pet-peeve of mine that velocities are vectors and rarely treated as such. I guess it's my physics background. All I could think about for k+98 was all of the other real considerations that would be needed to solve such a problem in real life versus the friction free, force free, instantaneous velocity, infinite acceleration capable trains in question. Please excuse me for these faults, I meant no harm.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Problem # k +

From 3 men and 4 women, three persons are to be selected

in such a way that at least one woman is selected. In how many

different ways can they be selected?

Character is who you are when no one is looking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

Ricky, try again!

Problem # k + 101

Prove that n! + 1 is composite for infinitely many values of n where n is a positive integer.

Character is who you are when no one is looking.

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**rimi****Member**- Registered: 2006-02-21
- Posts: 17

For the problem K+100 the answer should be 34..

(4C1*3C2)+(4C2*3C1)+(4C3*3C0)=12+18+4=34

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,418

After a long time, here's solution to Problem # k + 42

Problem # k + 42

On a deserted island live five people and a monkey. One day everybody gathers coconuts and puts them together in a community pile, to be divided the next day. During the night one person decides to take his share himself. He divides the coconuts into five equal piles, with one coconut left over. He gives the extra coconut to the monkey, hides his pile, and puts the other four piles back into a single pile. The other four islanders then do the same thing, one at a time, each giving one coconut to the monkey to make the piles divide equally. What is the smallest possible number of coconuts in the original pile?

**The smallest solution is 3121 coconuts in the pile.**

Character is who you are when no one is looking.

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