Always Perfect
Age 14 to 18
Challenge Level
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Common Divisor
Age 16 to 18
Challenge Level
Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
Polite Numbers
Age 16 to 18
Challenge Level
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Maths Makes A Difference
Age 14 to 18
Recording and links to the resources used during the MMAD webinar on 2nd February 2021.
Digital Equation
Age 16 to 18
Challenge Level
Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?
Curve Hunter
Age 14 to 18
Challenge Level
This problem challenges you to sketch curves with different properties.
Exploring Cubic Functions
Age 14 to 18
Challenge Level
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Curve Fitter
Age 14 to 18
Challenge Level
This problem challenges you to find cubic equations which satisfy different conditions.
Curvy Equation
Age 16 to 18
Challenge Level
This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.
NRICH is part of the family of activities in the Millennium Mathematics Project.