Math Is Fun Forum

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Hands of the clock..

I've been pounding my head on this but in vain..

At what time (exact or approximate), after noon, the three hands of a clock are at equal angles to each other?:D

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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Hands of the clock..

Well.. After a bit of easy calculations, all i can figure out is that after 240/11 (i.e. 21+9/11) minutes, the hour & minute hands will be at 120` & so an APPROXIMATE answer would be somewhere around 12:21....!
But i just can't figure out the EXACT answer!?

Last edited by ZHero (2008-06-29 07:27:37)

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If two or more thoughts intersect, there has to be a point!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Hands of the clock..

There aren't any times when all three hands are exactly 120° away from each other.
I proved this by finding all times when the minute and hour hands were the right distance apart, then exhaustively checking the second hand's position at each of these times. None fit.

I'm pretty sure there's a better proof though.

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Why did the vector cross the road?
It wanted to be normal.

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Hands of the clock..

Wow! So may there be other such SPECIFIC positions that CANNOT occur amidst the three hands of a clock! I wonder if there be a GENERAL RULE stating which angles are really formed and which never!!?
Its getting pretty interesting (for your statement to be true mathsy)!!

Last edited by ZHero (2008-06-29 09:44:51)

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If two or more thoughts intersect, there has to be a point!