Christmas Streak 62/88: Clock #1

Logic Level 3

During a whole day, how many times do the hour hand and the minute hand of a clock form a 9 0 ∘ 90^{\circ} angle?

Details and assumptions:

  • A day is 24 hours.

  • The minute hand and the hour hand of the clock move perfectly continuously.

This problem is a part of <Christmas Streak 2017> series .

4 26 44 48 52 22 2 24

Boi (보이) by Boi (보이) , 19, South Korea

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2 solutions

Boi (보이)
Dec 2, 2017

Notice that in an hour, they forming a 9 0 ∘ 90^{\circ} angle happens exactly twice.

Then is the answer 48 48 ?

Nope, we have to exclude 3 : 00 , 9 : 00 , 15 : 00 , 21 : 00 3:00,~9:00,~15:00,~21:00 once cause it's duplicated.

So the answer is 44 . \boxed{44}.

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Ankur Gupta
Dec 3, 2017

One hour-2 times In 12 hour-22times In 24 hour=44 times . In 12 hour a day ,It's because at 3-4 and 9-10 timings are 90 degree only once while rest of time its is 2 times 90 degree .

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