Subtraction Surpriselive
Age 7 to 14
Challenge Level
Try out some calculations. Are you surprised by the results?
Non-transitive Dicelive
Age 11 to 14
Challenge Level
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Pair Productslive
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Pick's Theoremlive
Age 14 to 16
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.
Square Remainderslive
Age 16 to 18
Challenge Level
What is the remainder if you divide a square number by $8$?
Divisible Factorisationslive
Age 16 to 18
Challenge Level
Can you show that $n^5-n^3$ is always divisible by $24$?
Square Differencelive
Age 16 to 18
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?
Proper Factorslive
Age 16 to 18
Challenge Level
Can you find the smallest integer which has exactly 426 proper factors?
NRICH is part of the family of activities in the Millennium Mathematics Project.