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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

**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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi ShivamS and bobbym,

The solutions #4975 and #4976 are correct. Marvelous!

#4977. If

and , find the value of .#4978. If a + b + c = 13,

, find the value ofab + bc + ca.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

**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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym,

The solutions #4977 and #4978 are correct. Excellent!

#4979. If

and x + y = 3z, then find the value of z.#4980.

Character is who you are when no one is looking.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

**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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi anonimnystefy and bobbym,

The solution #4980 is perfect, anonimnystefy! Excellent!

bobbym, I made a mistake in the problem; regretted.

#4981.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym,

The solution #4981 is perfect. Splendid!

#4982. Find the value of x

.#4983

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym,

#4984. How many pieces of 85 cm length can be cut from a rod 42.5 meters long?

#4985.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym,

The solution [hide=#4984]I get 50.

Number of pieces = 42.5 x 100/85 = 4250/85 = 50

The solution #4985 is perfect. Exemplary!

PS : Thanks for the replies. I shall post 'English Language Puzzles' soon.

#4986.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**Denominator****Member**- Registered: 2009-11-23
- Posts: 155

Hello

Thanks

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym and Denominator,

The solution #4986 is correct. Stupendous!

#4987. If

, then what is the value of?

#4988. Given

and ,find the value of .

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym,

The solutions #4987 and #4988 are correct. Magnificent!

#4989.

#4990.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

I need a little explanation on how 4990 can be done in about 10 seconds.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

It can be shortened algebraically but still required a calculator.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

Okay, because I thought I was missing something.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,542

I can not even write the problems down in less than a minute. 10 seconds, I am too slow for that.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,428

Hi bobbym and ShivamS,

I made a mistake owing to my poor vision. The problem actually stated:

#4990.

The corrected version :

#4990.

Inconvenience regretted!

Character is who you are when no one is looking.

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