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
  • Designing a Polynomial 01/12/1999 00:00
    Can you find a polynomial function whose first derivative is equal to the function?
  • Can You Find... Trigonometry Edition 01/04/2015 00:00
    What graphs can you make by transforming sine, cosine and tangent graphs?
  • Equation or Identity (1) 01/04/2015 00:00
    Which of these equations concerning the angles of triangles are always true?
  • Equation or Identity (2) 01/04/2015 00:00
    Here are some more triangle equations. Which are always true?
  • Have a Sine 01/04/2015 00:00
    There's much more to trigonometry than sin, cos and tan...
  • The Quintessential Proof 01/03/2015 00:00
    In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.
  • Finding Circles 01/03/2015 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?
  • The Circle of Apollonius... Coordinate Edition 01/03/2015 00:00
    Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?
  • Nine Eigen 01/02/2011 00:00
    Explore how matrices can fix vectors and vector directions.
  • 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.
  • 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.
  • 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.
  • Factorial Fragments 01/12/2014 00:00
    Here you have an expression containing logs and factorials! What can you do with it?
  • Giants Poster 01/09/2014 00:00
  • Which Quadratic? 01/09/2014 00:00
    In this activity you will need to work in a group to connect different representations of quadratics.
 Scientific American - Math
  • A Belated Apology to Mozart and Modular Arithmetic 28/06/2015 03:00
    What do Mozart and modular arithmetic have in common? I used to think I didn't like them. I'm sorry, Mozart and modular arithmetic. Please forgive me.

    -- Read more on ScientificAmerican.com
  • Mathematical Art Takes a Fresh Look at Wallpaper 26/06/2015 13:00
    A mathematician shares new strategies for making patterns with repeating symmetries

    -- Read more on ScientificAmerican.com
  • What Is the Famous Monty Hall Problem? 24/06/2015 14:00
    Ever heard of the Monty Hall problem? If so, did the world famous brain teaser leave you flummoxed? If not, how does getting flummoxed—and then just as quickly un-flummoxed—sound?...

    -- Read more on ScientificAmerican.com
  • LEGO Adds More Women in Science to Its Lineup 24/06/2015 12:00
    The toy company has taken significant steps to address consumer interest in the addition of more female characters in STEM fields

    -- Read more on ScientificAmerican.com
  • Restore Research to Preserve the American Dream 23/06/2015 16:54
    Norman Augustine, former CEO of Lockheed Martin and former undersecretary of the Army talks about the report he co-chaired for the American Academy of Arts & Sciences, "Restoring the...

    -- Read more on ScientificAmerican.com
  • 100 Years of Great Physics: Watch Live Monday and Tuesday [Video] 22/06/2015 18:00
    General relativity and Noether’s theorem take center stage in two live Web broadcasts this week

    -- Read more on ScientificAmerican.com
  • A Few of My Favorite Spaces: Cantor's Leaky Tent 20/06/2015 22:00
    The mathematical space called Cantor's leaky tent is connected but just barely: remove one point, and the whole thing falls apart.

    -- Read more on ScientificAmerican.com
  • Furor over Tim Hunt Must Lead to Systemic Change 15/06/2015 22:50
    Condeming one man's sexist comments is not enough; we also need to affect broader change for women in science

    -- Read more on ScientificAmerican.com
  • Why Tim Hunt's Sexist Comments Were No "Joke" 15/06/2015 22:45
    The British Nobel Prize-winner has complained that he's been treated unfairly, but it is the women he insulted that deserve sympathy and support

    -- Read more on ScientificAmerican.com
  • Take a Bite out of the Math of Math 03/06/2015 00:12
    Mathematician Eugenia Cheng, tenured in the School of Mathematics and Statistics at the University of Sheffield in the U.K. and currently Scientist in Residence at the School of the Art Institute of...

    -- Read more on ScientificAmerican.com
  • When the <i>Mona Lisa</i> Is NP-Hard 31/05/2015 16:30
    Bob Bosch and Tom Wexler have developed a new way to make your favorite masterpieces into connect-the-dots puzzles. All you need is a little bit of quantification and a lot of computing time.

    -- Read more on ScientificAmerican.com
  • A Few of My Favorite Spaces: The Topologist's Sine Curve 28/05/2015 22:00
    The topologist's sine curve is a classic example of a space that is connected but not path connected: you can see the finish line, but you can't get there from here.

    -- Read more on ScientificAmerican.com
  • John Nash, Mathematician Who Inspired "A Beautiful Mind", Killed in Car Crash 24/05/2015 18:25
    The Nobel Prize winner was killed in a car crash along with his wife in New Jersey, state police said on Sunday

    -- Read more on ScientificAmerican.com
  • 25 Terrific Science(y) Books 20/05/2015 16:21
    John Horgan lists 25 of his favorite science(y) books, from Freud's The Interpretation of Dreams to Joyce's Ulysses

    -- Read more on ScientificAmerican.com
  • Moore's Law Keeps Going, Defying Expectations 19/05/2015 22:00
    It’s a mystery why Gordon Moore’s “law,” which forecasts processor power will double every two years, still holds true a half century later

    -- Read more on ScientificAmerican.com
  • Grapefruit Math 19/05/2015 13:00
    Spherical geometry: it's part of this complete breakfast.

    -- Read more on ScientificAmerican.com
  • The Equation for a Happy Mother's Day 06/05/2015 14:00
    What's the most important holiday in May? Obviously it's Mother's Day. But did you know there's an equation that can help you celebrate Mom? Keep on reading to find out what it is!

    -- Read more on ScientificAmerican.com
  • Star Wars Day: May the Fourth Be with You 02/05/2015 17:57
    16-year-old Paul Vermeesch recreate the impossible structures in M.C. Escher's Relativity--but with a Star Wars theme--in LEGO.

    -- Read more on ScientificAmerican.com
  • 5 Instagram Tips for Science Artists 29/04/2015 18:30
    I’ve been on Instagram for a long time, with a private account to share family photos with friends. Last year, I decided to start up a second account, @FlyingTrilobite, to share my art in...

    -- Read more on ScientificAmerican.com
  • The Truth Behind the Math: The Surprising Path of a Theorem [Q&A] 27/04/2015 20:00
    Mathematician Cédric Villani shares the actual conversations, emails and even dreams that led to his Fields Medal-winning proof

    -- Read more on ScientificAmerican.com
  • Book Review: Birth of a Theorem 24/04/2015 20:00
    Books and recommendations from Scientific American

    -- Read more on ScientificAmerican.com
  • In Praise of Fractals and Poetry 20/04/2015 18:00
    This year for Math Poetry month, I read Proportions of the Heart: Poems that Play with Mathematics, a collection of poems by Emily Grosholz.

    -- Read more on ScientificAmerican.com
  • Scientists Perturbed by Loss of Stat Tools to Sift Research Fudge from Fact 16/04/2015 15:30
    The journal Basic and Applied Social Psychology recently banned the use of p-values and other statistical methods to quantify uncertainty from significance in research results

    -- Read more on ScientificAmerican.com
  • Boots or Heels: My Wardrobe Paradox as a Woman in STEM 14/04/2015 14:17
    A couple of weeks ago a wonderful hashtag was making its way around Twitter, with female scientists all over the world sharing photos of their feet to show a day #InMyShoes.

    -- Read more on ScientificAmerican.com
  • Was I Wrong about “The End of Science”? 13/04/2015 15:29
    One of the coolest—and most stressful–moments of my career took place November 7, 1996, when I was a staff writer for Scientific American.

    -- Read more on ScientificAmerican.com