How many times in a day do the hands of a clock form a straight line but point in opposite directions ?
22
The hands are opposite (180° apart) once in every \(\frac{12}{11}\) hours, i.e. 11 times in 12 hours.
The usual 12 is reduced to 11 because between 5 and 7 o'clock the hands are opposite only once, at exactly 6 o'clock, so one occurrence is lost in every 12 hours.
In a day (24 hours): \(11 \times 2 = 22\) times. Check: 24 ÷ \(\frac{12}{11}\) = 22.
Hence, 22.
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