Three Neighbourslive
Age 7 to 14
Challenge Level
Take three consecutive numbers and add them together. What do you notice?
Adding Odd Numberslive
Age 11 to 16
Challenge Level
Is there a quick and easy way to calculate the sum of the first 100 odd numbers?
Where Are the Primes?live
Age 11 to 16
Challenge Level
What can we say about all the primes which are greater than 3?
Three Consecutive Odd Numberslive
Age 11 to 16
Challenge Level
How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?
What Does it All Add up To?live
Age 11 to 18
Challenge Level
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
Different Productslive
Age 14 to 16
Challenge Level
Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Impossible Sumslive
Age 14 to 18
Challenge Level
Which numbers cannot be written as the sum of two or more consecutive numbers?
Difference of Odd Squareslive
Age 14 to 18
Challenge Level
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
KS5 Proof Shortslive
Age 16 to 18
Challenge Level
Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).
Direct Logiclive
Age 16 to 18
Challenge Level
Can you work through these direct proofs, using our interactive proof sorters?
Secondary Toughnutslive
Age 11 to 18
Challenge Level
These secondary problems have not yet been solved. Can you be the first?
NRICH is part of the family of activities in the Millennium Mathematics Project.