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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

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

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
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Johnny, great work! You got it right! **Congratulations!!!**

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

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!**

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

#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.

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

$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!*

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

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.*

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

#42,

TheDude,

Solution is right! Proof is perfectly acceptable, right!

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

mathsyperson,

Yes. x is restricted to Natural numbers.

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

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!**

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

#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?

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

Solution to #43.**Excellent, TheDude!!! Keep it up!!!**

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

#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?

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

#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 ?

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

Solutions to #44 and #45:-

Excellent, JohnnyReinB and Identity!!!

Your answers are perfectly correct!!!

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

#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?

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,117

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

Truth alone triumphs - Mundaka Upanishad.

Character is who you are when no one is looking.

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