Puzzles
7 December
What is the obtuse angle in degrees between the minute and hour hands of a clock at 08:22?
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Every hour, the hour hand moves 360÷12 = 30°.
Every minute, the hour hand moves 30÷60 = ½° and the minute hand moves 360÷60 = 6°.
At 8:22, the hour hand will be 8×30+22×½ = 251° from the top of the clock
and the minute hand will be 22×6 = 132° from the top of the clock. The angle between the hands will
be 251-132 = 119°.
2 December
In a week (Monday 12:01 to Monday 12:01 a week later), how many times will the minute hand of an analogue clock point in the same direction as the hour hand?
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In a 12 hour period, the hands will meet at 12:00, between 1 and 2, between 2 and 3, ..., between 9 and 10 and between 10 and 11. This is 11 times.
Therefore in a week, the hands will meet 154 times.
