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Omni-MATH / 3n people forming n families of a mother, a father and a child, stand in a circle. Every two neighbours can exchange places except the case when a parent exchanges places with his/…

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problem

3n3n people forming nn families of a mother, a father and a child, stand in a circle. Every two neighbours can exchange places except the case when a parent exchanges places with his/her child (this is forbidden). For what nn is it possible to obtain every arrangement of those people by such exchanges? The arrangements differing by a circular shift are considered distinct.
Plain-text mathematical notation (without MathML)
3n people forming n families of a mother, a father and a child, stand in a circle. Every two neighbours can exchange places except the case when a parent exchanges places with his/her child (this is forbidden). For what n is it possible to obtain every arrangement of those people by such
exchanges? The arrangements differing by a circular shift are considered distinct.
Original LaTeX notation
$3n$ people forming $n$ families of a mother, a father and a child, stand in a circle. Every two neighbours can exchange places except the case when a parent exchanges places with his/her child (this is forbidden). For what $n$ is it possible to obtain every arrangement of those people by such
exchanges? The arrangements differing by a circular shift are considered distinct.

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Source and history

task_id
cc214294-4004-5f82-ac68-48ae72819af9
task_key
test--cc214294-4004-5f82-ac68-48ae72819af9
task_revision_id
1
config / split
/ test

Official source

initial import