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'Robo-turn' printed from https://nrich.maths.org/
45m
The total angle turned through after each of the first 4 moves is
$10^{\circ}$, $30^{\circ}$, $60^{\circ}$ and $100^{\circ}$. So the
robot does not face due East at the end of a move in its first
complete revolution. The total angle it has turned through after
each of the next 5 moves is $150^{\circ}$, $210^{\circ}$,
$280^{\circ}$, $360^{\circ}$ and $450^{\circ}$, so at the end of
the 9th move the robot
does face due East. As the robot moves
5m in each move, the distance it travels is 45m.
Note that this solution assumes that the robot is not starting the
process close to the North Pole!