A mad robot sets off towards the North East on a journey from the point (0,0) in a coordinate system. It travels in stages by moving forward and then rotating on the spot. It follows these pseudo-code instructions:

SUB JOURNEY

DISTANCE = 1000

WHILE (DISTANCE > 0.001)
MOVE DISTANCE
STOP
ROTATE(90, DEGREES, CLOCKWISE)
DISTANCE = DISTANCE / 2
END WHILE

EXPLODE

END SUB

Where does the robot explode?

This problem comes from our sister site NRICH, which is packed with challenges, activities and articles for maths learners and teachers.

We will publish a solution next month.