Hi friends. Well I am just going to post this note to start the problem chaining once again. The first one started by Calvin Lin . Hope this new thread will also receive the same response as the first one. For the new ones on brilliant I will tell the rules in short.

1) In each section there is a topic related to Algebra, Number theory, Combinatorics , Geometry, Calculus, Chemistry, Physics, Biology, etc.

2) First a question will be posted and then the viewers will have to answer the problem.Please avoid posting the same solution again and again.If you have a new solution, then you can post it.

3) After posting the solutions, You have to post a question in the end of your comment of solutions in order to continue the chain.

4) Also the problem writer can write the solution to the problems after 4 days in order to continue the chain.

In this way there will be a stream of questions for the people any many will be able to learn new ways of solving problems. If you solve the problem then you will receive +1 point. At the end of the week , a table showing the scores of people will be posted ( inspired from CMC). Thus you can get an opportunity to solve 'To Prove' types of problems and you will have various problems to solve. And please share this post in order to keep this post alive. ALL THE BEST and try your best. Thanks.

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`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewest\( Biology \)

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where is biology???

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Open for you to post the ques

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\( Chemistry \)

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\(Physics\)

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\( Combinatorics \)

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Find all whole numbers equal to sum of the squares of their digits .

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\( Inequalities \)

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Let \( a,b,c,d \) be positive real numbers such that \( \frac{1}{1+a^4}+\frac{1}{1+b^4}+\frac{1}{1+c^4}+\frac{1}{1+d^4}=1 \)

Then Prove that \( abcd≥3 \)

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\( Calculus \)

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Find the area enclosed under the curves \( y^2=x \) and \( y=x \) ??

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\(Geometry\)

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\( Number\) \(Theory \)

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Find the value of:

\[\frac{1+9999^4+10000^4}{1+9999^2+10000^2}\]

WITHOUT USING A CALCULATOR! Explain how you did it at the end

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\( Algebra\)

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Solve the following system of equations

\(\frac{2x^2}{1+x^2}=y^2 \)

\( \frac{2y^2}{1+y^2}=z^2 \)

\( \frac{2z^2}{1+z^2}=x^2 \)

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Err, where is Combinatorics?

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Up there..

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It wasn't there before.

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