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Absurdity Again

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?

Sweeping Satellite

Age 16 to 18 Challenge Level:

Hint 1: Gravitational potential energy is the integral of the gravitational force, and evaluates to a negative number, theoretically being zero when infinitely far away.

Hint 2: In the Newtonian gravitational field equation, it can be shown that $GM = gR^2$. That assumes a spherical body of course.