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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,775

Jane Fairfax, I wanted non primes only.

Sometimes they are also referred to as composite numbers. I was just trying to be clear in my question what non primes are. Okay, I shall make it non primes alone. Thanks for correcting me.

Sometimes, in my over enthusiasm I make mistakes. Thanks for correcting me, Jane Fairfax

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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**JohnnyReinB****Member**- Registered: 2007-10-08
- Posts: 453

well, since no one answered this question I'm looking at...

*"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted" *

Nisi Quam Primum, Nequequam

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Johnny, great work! You got it right! **Congratulations!!!**

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
- Posts: 47,775

Replies to #33, #37 and#38

mathsyperson is absolutely correct! All the answers you posted are bull's eye.

And you remember right. Long back, this question (#38) was posted by me.

**Well done, mathsy! Keep it up!**

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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#41. Create a 4X4 Magic Square using the numbers 1-16 without referring. If you can do it in less than five minutes, thats a very good performance.

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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$42. We all know the product of a number is maximum when the number is divided into equal parts.**. The question is, how many equal parts?**

*PS:- Time limit :- 15 daysAfter 15 days, if there are no replies or no CORRECT replies, I shall post the solution in EULER Avenue!*

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

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,775

Solution to #42.

Very good, Identity!!!!!

You are correct! You hit the bull's eye!

*I shall wait for some time, say 15 days for the proof now.*

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

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

*Last edited by TheDude (2007-11-09 03:16:14)*

Wrap it in bacon

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,775

#42,

TheDude,

Solution is right! Proof is perfectly acceptable, right!

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

Surely in that proof, x needs to be restricted to the naturals? That complicates things a bit.

Why did the vector cross the road?

It wanted to be normal.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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mathsyperson,

Yes. x is restricted to Natural numbers.

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: 47,775

Solution to #42.

Outstanding, TheDude! I wholeheartedly accept your proof.

The solution is,

into as many parts as when the parts are closest to e.

The proof, the solution are given supra.

Example:- Question :Divide 10 into equal parts such that the produce is the maximum.

Solution :

Two parts

10/2 = 5

Product 5x5=25.

Three parts

10/3=3.3333=10/3 approximately.

Product 10/3 x 10/3 x 10/3 = 1000/27. = 37 approximately

Four parts

10/4=2.5

Product = 10/4 x 10/4 x 10/4 x 10/4 = 10000/256 = 39.0625

Five parts

10/5=2

Product = 2x2x2x2x2 = 32.

Six parts

10/6 = 1.66666

Product = 10/6 x 10/6 x 10/6 x 10/6 x 10/6 x 10/6 = 1000000/46656 = 21.43 approximately.

The number of parts close to e, that is the natural logarithm base, of value 2.71828 roughly, are 2.5 and 3.33333 when divided into 4 equal parts and 3 equal parts respectively. Of the two of them, it is clear 2.5 is closer to 2.71828 than 3.3333.

**Therefore, the product is the greatest when the number 10 is divided into 4 equal parts. As given above, the product is 39.0625, visibly, which is the highest of all.**

The number e appears where we expect it least in Mathematics. This question and proof is intended to show the fact. To a novice or a layman, it would be immensely suprising to know that an irrational number would have anything to do with the seemingly simple question. As a matter of fact, the obvious reply to the question would have been 2 parts. Mathematics is a subject which requires a degree of certainity to a much greater level. I am pleased that the question has been solved in such a short duration. **Commendabl performance, TheDude and Identity!**

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

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

Thanks, but it was just an curiosity I remembered from somewhere, before seeing TheDude's proof I wouldn't have a clue where to start!

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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#43. I have 1000 one cent coins. These have to be packed in ten plastic bags in such a way that I should be able to give away any number of cents from 1 to 1000 in bags alone. For example, after I have put the 1000 one cent coins in bags, I may be required to give away 1 cent, or 100 cents or 433 cents etc. The number may vary from 1 to 1000. I should not open the bags once the cents are put in the plastic bags and I have marked how many cents each bag contains. I should give away bags only. How would I distribute the 1000 on cent dimes in the ten plastic bags?

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

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

*Last edited by TheDude (2007-12-12 01:23:13)*

Wrap it in bacon

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Solution to #43.**Excellent, TheDude!!! Keep it up!!!**

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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#44. A goat is tied to one corner of a square plot of side 12m by a rope 7m long. Find the area it can graze?

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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#45. The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

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

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**JohnnyReinB****Member**- Registered: 2007-10-08
- Posts: 453

*"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted" *

Nisi Quam Primum, Nequequam

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Solutions to #44 and #45:-

Excellent, JohnnyReinB and Identity!!!

Your answers are perfectly correct!!!

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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#46. A farmer built a fence around his 17 cows, in a square shaped region. He used 27 fence poles on each side of the square. How many poles did he need altogether?

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

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**JohnnyReinB****Member**- Registered: 2007-10-08
- Posts: 453

*"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted" *

Nisi Quam Primum, Nequequam

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,775

**Absolutely right, JohnnyReinB! Very well done!!!**

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

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