We consider mysterious hidden symmetries of a classical non-holonomic kinematic model. The problem was not stated by Vladimir Arnold but, I hope, its study is in the spirit of the Arnold school. Moreover, I hope that some participants of the seminar would help to find a better geometric interpretation of these symmetries. The mathematical seminar organised by V.I. Arnold is devoted to several subjects of mathematics. It takes place on Fridays, at 14:30 hours, in the Seminar Room of the ICTP Main Building. Contact: uribe@ictp.it