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
• 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?
• Equation or Identity (1) 01/12/1999 00:00
Which of these equations concerning the angles of triangles are always true?
• Equation or Identity (2) 01/12/1999 00:00
Here are some more triangle equations. Which are always true?
• Have a Sine 01/12/1999 00:00
There's much more to trigonometry than sin, cos and tan...
• Factorial Fragments 01/12/2014 00:00
Here you have an expression containing logs and factorials! What can you do with it?
• 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.
• 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.
• Giants Poster 01/09/2014 00:00
• 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.
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.
In this activity you will need to work in a group to connect different representations of quadratics.
• Absolutely! 01/11/2014 00:00
• 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.
• Nine Eigen 01/02/2011 00:00
Explore how matrices can fix vectors and vector directions.
Scientific American - Math
• Scientists Perturbed by Loss of Stat Tool 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

• 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.

• 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.

• ScienceDebate Revs Up for 2016 Presidential Election 13/04/2015 14:32
This year, I've been very fortunate to be a part of the inaugural class of the Presidential Leadership Scholars (PLS) program, which brings together 60 leaders from around the country to work on...

• Mathematicians Chase Moonshine’s Shadow 07/04/2015 14:30
Researchers are on the trail of a mysterious connection between number theory, algebra and string theory

• Against April Fools' in Science Journalism 01/04/2015 15:10
My lowest point as a science journalist came before I even knew what a science journalist was. I was a young punk in an eighth-grade science class at Northwood Middle School in Greenville, South...

• The Cantor Function: Angel or Devil? 31/03/2015 13:00
When you're looking at it, it just stays there, constant and still. But if you turn your back for just an instant at a point in the Cantor set, the function grows impossibly quickly.

• 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...

• 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.

• 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...

• 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

• 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)

• 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

• 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...

• 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...

• 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

• 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...

• 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...

• 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

• 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.

• 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...

• 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...