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For a few weeks, I spend some time to solve a question from Project Euler each day. I liked it and noticed that it makes me motivated.

I wonder if there exists such a site with challenging questions on especially topics such as linear algebra and probability which I would like to be good at. Do you know any challenge site with varying levels of difficulties?

P.S: Math.SE is even a good challenging resource where you may get badges and reputation but I'm more interested in a site like Project Euler or Python Challenge. Besides, it is difficult for a learner to answer questions in Math.SE faster than the experts on the topic, so Math.SE is not a good fit for motivation I intend to mean.

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[This is a slight plug, and I'm opening to deleting my answer.]

When you're looking for a site, your ability level would heavily influence the type of questions that you are able to answer. Without knowing much more about your knowledge and abilities, we cannot direct you to relevant examples. I looked at the questions you posed, and one of them was "How many ways to choose teams of 3-3-4 out of 10". Most people will consider this an extremely basic application of the binomial (or multinomial) theorem, as you can see from the answers that you get. However, you also asked questions on the Frobenius norm, and singular values of a matrix, so it's uncertain what the breadth and depth of your mathematical knowledge is.

I am the Mathematics Challenge Master on and we provide weekly problem sets that are tailored to your ability level. Under the Geometry and Combinatorics topic (which includes probability), you will see several problems similar to the "choose teams" question that you posed. For the Algebra and Number Theory topic, some might be too simple given your knowledge, as we are mainly targeted at identifying talented high school students worldwide. We are planning on introducing the topic of linear algebra in the near future. Once again, there's a disclaimer that the problems might be too simple for you, given the kinds of questions that you are asking.

As a problem site, you will get 8 problems to work on every week. If you provide the correct numerical answer, there is a random chance that you will be asked to submit your solution. In the following week, student submitted solutions will be posted, so that you can learn from the different good approaches that were taken. In this way, you'd have sufficient time to work on the problems, without feeling forced to answer before someone else gets selected.

This is a problem taken from last week's Combinatorics set.

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I registered to, it is a very nice site. And it tests the users level via diagnostic test. That suits very well to what I'm asking actually. – Helen Jan 15 '13 at 18:06
By the way, I know quite a bit about the topics I listed, I'm not a real novice. The choosing problem I asked was something that I wanted to show my friend that she is wrong. – Helen Jan 15 '13 at 18:08

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