Challenge Level

Try out some calculations. Are you surprised by the results?

Challenge Level

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Challenge Level

What is the remainder if you divide a square number by $8$?

Challenge Level

Can you show that $n^5-n^3$ is always divisible by $24$?

Challenge Level

Can you find the smallest integer which has exactly 426 proper factors?

Challenge Level

Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?