When working on maths problems, it's often a good idea to start by trying out some examples using small numbers, and looking for patterns, before looking for general rules. In this set of tasks, we invite you to move from particular cases to generalisations, and use the power of algebra to prove your findings.
Multiple Surprises and Square Number Surprises include solutions that have previously been submitted to NRICH, so you may wish to try these problems first and then compare your approach with the published ones. Then try Tilted Squares and Difference of Two Squares, and send us your solutions!
problem
Favourite
Multiple surprises
Age
11 to 16
Challenge level
Sequences of multiples keep cropping up...
problem
Favourite
Square number surprises
Age
14 to 16
Challenge level
There are unexpected discoveries to be made about square numbers...
problem
Favourite
Tilted squares
Age
11 to 14
Challenge level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
problem
Favourite
Difference of two squares
Age
14 to 16
Challenge level
What is special about the difference between squares of numbers adjacent to multiples of three?