A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Charlie and Lynne put a counter on 42. They wondered if they could
visit all the other numbers on their 1-100 board, moving the
counter using just these two operations: x2 and -5. What do you
Which of these games would you play to give yourself the best possible chance of winning a prize?
Explore when it is possible to construct a circle which just
touches all four sides of a quadrilateral.
Is it really greener to go on the bus, or to buy local?
Can you make sense of these three proofs of Pythagoras' Theorem?
Investigate the properties of quadrilaterals which can be drawn
with a circle just touching each side and another circle just
touching each vertex.
Harry sent us a very clear algebraic solution to this problem, and
we also received lots of ideas on how to solve it numerically.
Go to last month's problems to see more solutions.
This fascinating article delves into the world of talk in the
classroom and explains how an understanding of talking can really
improve the learning of mathematics.
This article stems from research on the teaching of proof and
offers guidance on how to move learners from focussing on
experimental arguments to mathematical arguments and deductive