Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Explore the two quadratic functions and find out how their graphs are related.

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Here are some more quadratic functions to explore. How are their graphs related?

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

Several of you worked out methods of calculating the number of L triominoes needed to tile different sizes of L triominoes.

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.