Here is a site that updates puzzles regulalry:
 mathschallenge.net
  • Irrationality Of E 17/10/2010 01:00

    Prove that e is irrational.

    Problem ID: 377 (17 Oct 2010) / Difficulty: 4 star
  • Rectangle Construction 17/10/2010 01:00

    Find the connection between the constructed length and the original rectangle.

    Problem ID: 376 (17 Oct 2010) / Difficulty: 2 star
  • Inscribed Circle In Isosceles Triangle 16/08/2010 01:00

    Find the radius of the circle inscribed inside the isosceles triangle.

    Problem ID: 375 (16 Aug 2010) / Difficulty: 2 star
  • Multiplying Magic Square 16/08/2010 01:00

    Show how the values 1, 2, 4, 8, 16, 32, 64, 128, and 256 can be placed in a 3x3 square grid so that the product of each row, column, and diagonal gives the same value.

    Problem ID: 374 (16 Aug 2010) / Difficulty: 3 star
  • Polynomial Roots 07/08/2010 01:00

    Prove that the roots of the polynomial, xn + cn-1xn-1 + ... + c2x2 + c1x + c0 = 0, are irrational or integer.

    Problem ID: 373 (07 Aug 2010) / Difficulty: 3 star
  • Hops And Slides But Never Square 07/08/2010 01:00

    Prove that the minimum number of moves to completely reverse the positions of the coloured counters can never be square.

    Problem ID: 372 (07 Aug 2010) / Difficulty: 3 star
  • Irrationality Of Pi 24/12/2009

    Prove that π is irrational.

    Problem ID: 371 (24 Dec 2009) / Difficulty: 4 star
  • Square And Round Plugs 24/12/2009

    Which fits better... a round plug in a square hole or a square plug in a round hole?

    Problem ID: 370 (24 Dec 2009) / Difficulty: 2 star
  • Algebraic Cosine 30/11/2009

    Prove that cos(x) is algebraic if x is a rational multiple of Pi.

    Problem ID: 369 (30 Nov 2009) / Difficulty: 4 star
  • Inscribed Square 30/11/2009

    Find the side length of the square inscribed inside the right angled triangle.

    Problem ID: 368 (30 Nov 2009) / Difficulty: 2 star
  • Infinite Circles 15/11/2009

    What fraction of the large red circle do the infinite set of smaller circles represent?

    Problem ID: 367 (15 Nov 2009) / Difficulty: 4 star
  • Factorial Fragments 01/12/2014 00:00
    Here you have an expression containing logs and factorials! What can you do with it?
  • Transformation ... or Not? 01/01/2015 00:00
    This graph looks like a transformation of a familiar function...
  • Absolutely! 01/11/2014 00:00
    What can you say about this graph? A number of questions have been suggested to help you look at the graph in different ways. Use these to help you make sense of this and similar graphs.
  • Two-way Functions 01/11/2014 00:00
    This gives you an opportunity to explore roots and asymptotes of functions, both by identifying properties that functions have in common and also by trying to find functions that have particular properties. You may like to use the list of functions in the Hint, which includes enough functions to complete the table plus some extras.You might like to work on this problem in a pair or small group, or to compare your table to someone else's to see where you have used the same functions and where not.
  • Approaching Asymptotes 01/11/2014 00:00
    Can you describe what an asymptote is? This resource includes a list of statements about asymptotes and a collection of graphs, some of which have asymptotes. Use the graphs to help you decide whether you agree with the statements about asymptotes.
  • Picture the Process I 01/11/2014 00:00
    How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane? After sketching graphs for these and other real-world processes, you are offered a selection of equations to match to these graphs and processes.
  • Finding Circles 01/12/1999 00:00
    Can you find the centre and equation of a circle given a number of points on the circle? When is it possible and when is it not?
  • Quadrature of the Lunes 01/12/1999 00:00
    A lune is the area left when part of a circle is cut off by another circle. Can you work out the area?
  • The Quintessential Proof 01/12/1999 00:00
    In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.
  • The Circle of Apollonius... Coordinate Edition 01/12/1999 00:00
    Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?
  • Discriminating 01/09/2014 00:00
    You're invited to decide whether statements about the number of solutions of a quadratic equation is always, sometimes or never true.
  • Giants Poster 01/09/2014 00:00
  • Factorisable Quadratics 01/09/2014 00:00
    This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.
  • Which Quadratic? 01/09/2014 00:00
    In this activity you will need to work in a group to connect different representations of quadratics.
  • Nine Eigen 01/02/2011 00:00
    Explore how matrices can fix vectors and vector directions.
 Scientific American - Math
  • A Few of My Favorite Spaces: The Cantor Set 26/03/2015 12:30
    Last month, I wrote about the -Base, a website that serves a similar function to the book Counterexamples in Topology. I'm teaching a topology class this semester, and it's been fun to revisit some...

    -- Read more on ScientificAmerican.com
  • The Science of TED 2015 23/03/2015 14:00
    What I love about the annual TED gathering in Vancouver is the way science coexists along with art, social justice, popular song and the rest of TED's eclectic mix.

    -- Read more on ScientificAmerican.com
  • What’s so Great about Continued Fractions? 17/03/2015 12:30
    The more I learn about continued fractions, the more enamored I am with them. Last week, when I wrote about how much better continued fractions are than the arbitrary decimal digits we usually use to...

    -- Read more on ScientificAmerican.com
  • The Best Pi Day Pies and Celebrations 16/03/2015 20:45
    Reader-submitted photos of pi pies, pizzas and parties to commemorate the Pi Day of the Century

    -- Read more on ScientificAmerican.com
  • Irrational Exuberance: How Will You Celebrate the Pi Day of the Century? 14/03/2015 13:26
    Send us pix of your pies, pizzas and parties in honor of math (and circular baked goods)

    -- Read more on ScientificAmerican.com
  • The Pi Day of the Century 13/03/2015 13:15
    The first five digits of pi, 3.1415, is being celebrated on March 14, 2015, with a day for math fun, circular logic and, of course, pie eating

    -- Read more on ScientificAmerican.com
  • American Pi: Why the Day Belongs to the U.S. (and Belize) 12/03/2015 13:54
    Pi may be a universal constant, but only two countries can natively celebrate Pi Day: the U.S. and Belize. That's because they are the only ones (if Wikipedia is correct) to shorthand their date...

    -- Read more on ScientificAmerican.com
  • Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead. 11/03/2015 12:30
    The digits of pi reciting contest is an all-too-common Pi Day event. And as this year is a once-in-a-century confluence of month/day/year with the first few decimal digits of pi, we might be in for...

    -- Read more on ScientificAmerican.com
  • A Glimpse into How Mathematicians Party [Excerpt] 06/03/2015 15:00
    Michael Harris’s book provides a colorful insider’s investigation of what pure mathematicians do and why they do it

    -- Read more on ScientificAmerican.com
  • Uber, but for Topological Spaces 01/03/2015 01:00
    So it's cold and rainy, and you're up a little too late trying to figure out why that one pesky assumption is necessary in a theorem. Wouldn't it be nice if you could just order up a space that was...

    -- Read more on ScientificAmerican.com
  • Things to Make and Do in the Fourth Dimension (Book Review) 26/02/2015 23:00
    Sometimes you want to learn a “new” multiplication algorithm from a general interest math book, sometimes you want to learn why voting systems are doomed to imperfection, and...

    -- Read more on ScientificAmerican.com
  • Game Theory Calls Cooperation into Question 23/02/2015 19:00
    A recent solution to the "prisoner's dilemma," a classic game theory scenario, has created new puzzles in evolutionary biology

    -- Read more on ScientificAmerican.com
  • It's Time for More Racial Diversity in STEM Toys 23/02/2015 18:00
    It’s clear that we as a nation are failing to engage minority students in science, technology, engineering, and mathematics as well as we could.

    -- Read more on ScientificAmerican.com
  • 15 Surprises about Scientific American 22/02/2015 17:52
    Scientific American's parent company, Macmillan Science & Education strives to be both a place where curious minds gather together to achieve great things for our customers—and where we...

    -- Read more on ScientificAmerican.com
  • Physics Week in Review (Valentine’s Edition): February 14, 2015 14/02/2015 10:43
    Today is Valentine’s Day. In love? Or just the opposite? Express how you feel with physics-inspired Valentines—and anti-Valentines for those who perhaps aren’t huge fans of the...

    -- Read more on ScientificAmerican.com
  • Is AI Dangerous? That Depends… 13/02/2015 16:38
    Somewhere in the long list of topics that are relevant to astrobiology is the question of ‘intelligence’. Is human-like, technological intelligence likely to be common across the universe?

    -- Read more on ScientificAmerican.com
  • Gauss and Germain on Pleasure and Passion 13/02/2015 13:30
    Sophie German, who was not allowed to attend university, was the first woman to make significant original contributions to mathematical research.

    -- Read more on ScientificAmerican.com
  • How to Choose the Form of an Infographic: It's All about Context 10/02/2015 14:00
    As a graphics designer, I have a love/hate relationship with circles. The humble form provides a relief from rigid rectangular chart structures that are pinned to x- and y-axes.

    -- Read more on ScientificAmerican.com
  • Strange Stars Pulsate According to the "Golden Ratio" 09/02/2015 14:30
    Astronomers have discovered variable stars that periodically dim and brighten at frequencies close to the famed golden mean

    -- Read more on ScientificAmerican.com
  • Cities Could Win Economically by Losing Olympics 06/02/2015 18:00
    According to sports economist Andrew Zimbalist, most cities that win the right to host the Olympics will spend far more to prepare for the games than they estimate in their winning bid. Steve Mirsky...

    -- Read more on ScientificAmerican.com
  • The Media and the Genius Myth 05/02/2015 14:00
    I’ve been thinking a lot about the genius myth, the notion that in order to be a successful in certain disciplines, you need to have a special innate talent that can’t be learned.

    -- Read more on ScientificAmerican.com
  • Understand the Measles Outbreak with this One Weird Number 31/01/2015 21:21
    15. That’s all you need to know about the measles. OK, that’s not true at all. There's no one weird trick that will give you a flat belly (besides lying face-down on something flat), and...

    -- Read more on ScientificAmerican.com
  • Does Mathematical Ability Predict Career Success? 29/01/2015 20:00
    A study that has tracked students exceptional in math for 40 years checks their accomplishments

    -- Read more on ScientificAmerican.com
  • Apply for Science Communication Awards, Fellowships and Internship Programs 29/01/2015 13:12
    Participation of broader audiences in science, technology, engineering, mathematics (STEM) requires engaging under-served audiences. The conduit of this engagement is communication.

    -- Read more on ScientificAmerican.com
  • 3 Super Bowl Fun Facts 28/01/2015 13:00
    Want to amaze your friends at that Super Bowl party you're going to? All you have to do is hit 'em with some Super Bowl math fun facts. Keep on reading to learn what they are!

    -- Read more on ScientificAmerican.com