我加工了一下的时钟问题

Suppose you have a clock with an hour hand and a minute hand which are indistinguishable. BOTH HANDS ONLY SWING FROM MINUTE MARK TO MINUTE MARK PERIODICALLY which means the minimum hand movement is 6 degree. How many moments are there, in the interval from noon to midnight (including noon but excluding midnight), where the time shown by the clock is ambiguous?

In the mean time is there any solution of 24x = x (mod 30) if 0 <= x <= 30 and x is an integer?