problem
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?
problem
Euler's totient function
Age
16 to 18
Challenge level
How many numbers are there less than $n$ which have no common factors with $n$?
problem
To swim or to run?
Age
16 to 18
Challenge level
The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?
problem
Tri-angled trig
Age
16 to 18
Challenge level
Can you justify this equation involving three angles?
problem
Square remainders
Age
16 to 18
Challenge level
What is the remainder if you divide a square number by $8$?
problem
Proper factors
Age
16 to 18
Challenge level
Can you find the smallest integer which has exactly 426 proper factors?
problem
Divisible factorisations
Age
16 to 18
Challenge level
Can you show that $n^5-n^3$ is always divisible by $24$?
problem
Square difference
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?
problem
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.
problem
The Tour de Clochemerle
Age
14 to 18
Challenge level
Can you work out where these 5 riders came in a not-quite-so-famous bike race?
problem
Amicable arrangements
Age
16 to 18
Challenge level
Three of Santa's elves and their best friends are sitting down to a festive feast. Can you find the probability that each elf sits next to their bestie?
problem
Frosty the Snowman
Age
16 to 18
Challenge level
Frosty the Snowman is melting. Can you use your knowledge of differential equations to find out how his volume changes as he shrinks?