Three clocks which show the times for three different time zones are hanging on a wall. The length of their minute hands is the same - but not the lengths of their hour hands. The lengths of the hour hands of clock 1, clock 2 and clock 3 are 7 cm, 14 cm and 21 cm respectively.
The clocks are arranged on the wall in such a way that the tips of their minute hands form an equilateral triangle at any point in time.
Clock 3 shows UTC. Which time zones clock 1 and clock 2 show such that under this condition the tips of the three hour hands also form an equilateral triangle at any point in time? Hint: There may be more than one solution.