Combinatorics

Can anyone give me some good combinatorics to study from? I have mathematical circles which is an amazing book but its level only takes you so far. Any other book for regional mathematics Olympiad will also be appreciated. I already have thrill of high school mathematics. Finally, what would you guys recommend for the Astronomy Olympiad I can solve most math and some physics problems but their actual astronomy questions baffle me like some brightest star of x constellation.

Easy Math Editor

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

what do they ask?

Fahad Shihab - 7 years, 8 months ago

For example 'Consider all the three element subsets of the set 1,2,3,4...299,300. Of this set how many three element subsets have the sum of their three elements divisible by three?

A Former Brilliant Member - 7 years, 8 months ago

You can try , Path to combinatorics for undergraduates by Titu Andreassu (You can google it , (very nice book)) .

Shivang Jindal - 7 years, 8 months ago

The practice->olympiad->combinatorics section here on Brilliant.org is a good starter, and free. As for books, I like Epp's Discrete Mathematics, which covers combinatorics and a lot more, and is quite readable. I'm presently working through it myself. ("Plodding" would be a more accurate term, but that's because of me, not the book.)

Christopher Johnson - 7 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$