Anyone has any source for interesting and difficult math problems?

It may seem a but restarted, but give figuring out calculus a try. Not just understanding it, but start with a simple idea and work your way to developing some Math to describe it! I had a pretty fun time figuring my way around Rate Of Change in graphs several years ago and it helped me a lot once I got to calc.

"Proofs from the book"

Define math problems.
Define fun.
Trying to understand real analysis is a problem and its fun.
On that matter, "real analysis" by rudin is my favourite.
Dessert it with some Measure theory and you will understand probability on a whole different level

>>7801942
Math problems like this one that my old math prof posted on fb: Suppose you have a 10cm needle and you are throwing it on a big lined paper with the lines being paralel and 10cm apart from eachother. How many times out of N throws is the needle going to touch at least one line?
He posted a bunch more in a pdf they were composed by some mathematitian (supposedly they were for kids but some of them were fucking hard as balls).

In programming competitions I used to go to in hs there were problems that were told as a story which I really liked cuz it added flavor and made it more fun, you know like there was a problem where a swallow was flying out of her nest and it flew out in a line to catch some worms, you had to tell her in which direction to fly to catch the most worms supposing the nest is in the middle of a coordinate grid a worms are straight lines represented by 2 points. We even had some where you had to figure out how to represent shit on your own but those were only done on paper as it would be hard to test for them.

I want something like that, but math... I only have some basic knowledge in analysis, linear algebra and discrete math. It would be cool if I had a problem where I had to figure out some special way to represent objects to solve it. But I have no idea if anything like what I want is out there, I'm no professional mathematician I just do this for fun.

>>7802051
You can take any math Olympics book. Some of them, if not all, have the answers.
http://olympiads.win.tue.nl/imo/books.html
I think this is the one we have in our library:
http://www.amazon.com/exec/obidos/ISBN=0817645462/theinternationscA/

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>>7801861

This isn't terribly hard but I had fun with it some months ago.

>>7801861
brilliant.org is a good last resort when you cant come up with your own math problems or don't have energy to find any

>>7801861
Here's one:

How many points on the half parabola y=x^2, with x>0, have rational distance?

Spoiler: this is a hard problem

>>7802408
What do you mean "have rational distance?" From zero?

>>7802474
Not him but it should mean that you can express the distance as a rational number.

>>7802474
Distance between any two points on that section of the parabola is a positive integer

>>7802539
Oops not integer lol, a nonzero rational number

>>7802408
infinite many?

>>7802141
This, and if the olympiad problems are too tough, look into AIME problems.

http://www.artofproblemsolving.com/wiki/index.php?title=AIME_Problems_and_Solutions

>>7802408
If you mean rational distance from 0, it's pretty trivial to show it's infinitely many.

Here's a problem that I like:

Suppose a coin is flipped repeatedly. What is the probably that the first instance of two consecutive heads precedes the first instance of three consecutive tails?