How many times in a 12-hour period do the hour hand and the minute hand of a correct clock make a right angle with each other?

The minute hand gains on the hour hand and forms a right angle twice in each hour, which suggests 24 times in 12 hours. However, near 3 o'clock and near 9 o'clock two of these coincide, so two of the 24 are counted twice. The correct count is 24 − 2 = 22 times in 12 hours (and 44 times in a full day).