Between $2$ o'clock to $10$ o'clock, how many times the hands of a clock are at right angle?

Using the standard clock rule, the hands of a clock are at a right angle exactly 22 times in a full 12-hour cycle. To find the occurrences between 2 o'clock and 10 o'clock, we subtract the instances occurring between 10 o'clock and 2 o'clock (wrapping around), which account for 8 right angles. This leaves exactly 14 right angles between 2 o'clock and 10 o'clock.

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