Hoots Math

Math extra credit help..? (by Friday)?

One owl hoots every 3 hours, a second owl hoots every 8 hours and a third owl hoots every 12 hours. If they all hoot at the start, how many times on the hour in 3 days will at least two owls not give a hoot at the same time?

66.

Assume they begin hooting in unison at 12 midnight.

Owls 1 and 3 hoot together at 12 noon.

Owls 1, 2, and 3 hoot together again at 12 midnight, starting the cycle over again.

That leaves 22 hours in the day where 1 or 0 owls hoot. Over 3 days, there are 66 times on the hour when at least two owls do not give a hoot at the same time.
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Edit:

The other answers seem to be counting the number of times that only 1 owl hoots. But surely if all three owls do not give a hoot on the hour, then at least two of them do not give a hoot?

Grrrr. Ekram’s a leech.

Husayn Halani Hunt Part 2