2 out of 3
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
2 out of 3
Use cunning to work out a strategy to win this game.
2 out of 3
At what angle should you throw something to maximise the distance it travels?
2 out of 3
Two cannons are fired at one another and the cannonballs collide... what can you deduce?
2 out of 3
This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
3 out of 3
Exponential functions grow pretty quickly...
3 out of 3
Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?
3 out of 3
Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.
3 out of 3
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
3 out of 3
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
