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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Problem # k + 99

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

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

I love that kind of problems.

IPBLE: Increasing Performance By Lowering Expectations.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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: 1,055

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.

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

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?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Ricky, try again!

Problem # k + 101

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

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.**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

For problem#K+101

It does not hold for n=2... as (2!+1)=3,which is a prime number.

Ganesh ,by infinitely many values of n , do you mean large values of n? Then what is the lower limit for n?

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

rimi, your solution to Problem # k + 100 is correct

In Problem # 101, infintely many values means an unending sequence. Like the list of prime numbers, powers of the number 2 etc. For both n=1, n=2, and n=3, the resultants are prime numbers. However, for n=4, n=5, n=6, n=7 etc., the value of n! + 1 is composite.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 102

Three-fourth of a number is equal to 60% of another

number, and the difference between the two numbers is 20. What

is the sum of the two numbers?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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

By taking the route of a - b = 20, instead of b - a = 20, you can also get an answer of -180.

Why did the vector cross the road?

It wanted to be normal.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

Nice catch mathsyperson, can I still be half right? Maybe it should have read, "What are the sums of the numbers?". Hey, did I just get tricked!?

*Last edited by irspow (2006-02-23 10:20:06)*

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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

You can be almost fully right, really. You did all the working, and I just stuck a little comment on the end. And I think the reason why ganesh didn't phrase it like that was because he missed it himself.

Why did the vector cross the road?

It wanted to be normal.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

mathsyperson is right! Although I explore the possibilites of other solutions, this time I didn't think of that

Well done, irspow and mathsyperson

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 103

A circle is inscribed within an equilateral triangle and another is circumscribed. Calculate the ratio of the area of the incircle to the circumcircle.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 104

What is the maximum slope of the curve y = -x³ - 3x² + 9x - 27 and what point is it?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Well done, mathsyperson

Problem # k + 105

A group of bess equal in number to the square root of half the whole swarm alighted on a jasmine bush, leaving behind 8/9 of the swarm. And only one bee circled a lotus for it was attracted by the buzzing of a sister bee that was so careless as to fall into the trap of the fragrant flower. How many bees were there in the swarm?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 106

Four brother have 45 Dollars. If the money of the first is inreased by 2 Dollars and the money of the second is decreased by 2 Dollars, and the money of the third is doubled and the money of the fourth is halved, then all of them will have the same amount of money. How much does each have?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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