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What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

Old Nuts

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

Operating Machines

Age 16 to 18 Challenge Level:

Have you carefully read the question?

What happens if you repeatedly apply DIFF to $f(x)=x$?

What happens if you repeatedly apply INT to $f(x)=x$?

What happens if you apply DIFF several times followed by INT several times?

What functions might you try instead of $f(x)=x$?