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# The Coc'ks Clock

## Question

The Rooster crows every time the hour hand points exactly between 1 and 2.
How many coock-a-doodle-doos shall it make from midnight till noon?

Edited by TimeSpaceLightForce

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I feel SO lame: The hour hand points halfway between 1 and 2 at 1:30 and at no other time, I would have thought. What am I missing?

(Light bulb goes off), it crows if the hour hand touches halfway between ANY 1 and ANY 2, either way around. So...

Since there are 5 instances of "1" and 2 instances of "2", and two ways (clockwise and counterclockwise) between each pair, there must be 20. Admittedly, I couldn't say where the two 1's of "11" are located, but presumably they aren't in the same place...

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What does "exactly between" mean?

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10-11:

1) 00:00
2) 00:30
3) 01:30
4) 11:00
5) 11:30

In each case, the opposite.

Depends whether you count 00:00 6:00 12:00 in the first case.

Edited by harey
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I think...two times

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@bonanova..Right question..its means pointing to the middle of an arc joining  1 and 2. I think the chicken can't figure that..but can view it as the "distance of  a 1 to hour hand's tip is equal to the distance of a 2 to the hour hand's tip".

@wg..i.e if both hands points to the middle

@harey..yes 0:00,6:00,12:00 are counted.. but it's more than eleven. Can you find the other?

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..that's all.

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