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
• Paired Parabolas 01/12/1999 00:00
Some parabolas are related to others. How are their equations and graphs connected?
• Nested Surds 01/05/2015 00:00
Can you find values that make these surd statements true?
• Can You Find... Trigonometric Edition Part 2 01/06/2015 00:00
Can you find trig graphs to satisfy a variety of conditions?
• Equation or Identity (2) 01/04/2015 00:00
Here are some more triangle equations. Which are always true?
• Curvy Cubics 01/06/2015 00:00
Use some calculus clues to pin down an equation of a cubic graph.
• Can You Find... Cubic Curves 01/06/2015 00:00
Can you find equations for cubic curves that have specific features?
• Name That Graph 01/12/1999 00:00
How can you work out the equation of a parabola just by looking at key features of its graph?
• Which Fraction Is Bigger? 01/12/1999 00:00
Given two algebraic fractions, how can you decide when each is bigger?
• Between 01/12/1999 00:00
If you know some points on a line, can you work out other points in between?
• Nine Eigen 01/02/2011 00:00
Explore how matrices can fix vectors and vector directions.
In this activity you will need to work in a group to connect different representations of quadratics.
• Factorial Fragments 01/12/2014 00:00
Here you have an expression containing logs and factorials! What can you do with it?
• 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.
• Giants Poster 01/09/2014 00:00
Scientific American - Math