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What happens when you straighten out concentric circles?
Can you make sense of this visual combinatorics proof?
This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
Find the smallest value for which a particular sequence is greater than a googol.
Choose any whole number n, cube it, add 11n, and divide by 6. What do you notice?
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!
What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
Consider these weird universes and ways in which the stick man can shoot the robot in the back.
An arithmetic progression is shifted and shortened, but its sum remains the same...
Can you make sense of this relationship between function and derivative?
Find the location of the point of inflection of this cubic.
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.
Can you interpret this algorithm to determine the day on which you were born?
What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?
Can you make sense of this combination of trig functions?
At what angle should you throw something to maximise the distance it travels?
Two cannons are fired at one another and the cannonballs collide... what can you deduce?
Can you work out what happens when this mad robot sets off?
What can you deduce about prime numbers in arithmetic progression?
Trigonometry, circles and triangles combine in this short challenge.
In this short challenge, can you use angle properties in a circle to figure out some trig identities?
Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
Can you solve this problem involving powers and quadratics?
Can you make sense of this paradoxical question?
Can you get to the root of this problem about surds?
Can you make all of these statements about averages true at the same time?
Can you invert this confusing sentence from Lewis Carrol?
Can you massage the parameters of these curves to make them match as closely as possible?