kangaroo math
Exam
Logical Reasoning
An equilateral triangle starts in a given position and is moved to new positions in a
sequence of steps. At each step it is rotated about its centre, first by 3◦
, then by a further 9◦
,
then by a further 27◦
, and so on (at the n-th step it is rotated by a further (3n
)
◦
). How many
different positions, including the initial position, will the triangle occupy? Two positions are
considered equal if the triangle covers the same part of the plane.
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