In this feature, the problems give you an answer or output, and you need to work out the question or input. Mathematicians call this an inverse problem, and inverse problems have applications in fields as diverse as seismology, medical imaging and diagnostics, and financial maths.
problem
A little light thinking
Age
14 to 16
Challenge level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
problem
Which spinners?
Age
14 to 18
Challenge level
Can you work out which spinners were used to generate the frequency charts?
problem
Data matching
Age
14 to 18
Challenge level
Use your skill and judgement to match the sets of random data.