hour and minute

[rahulshetty]

How many times do the hour and minute hand cross each other in a twelve hour period ?

[Fibonacci]

Between noon and midnight, the minute hand passes the hour hand 10 times. It does not pass in the hours from 12 to 1 p.m., and 11 p.m. to midnight.

[mjd]

Surely if you start at noon then the minute hand must cross the hour hand at: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 & 11 o'clock. Making 11 times.

[Otleybard]

Must go with Fibonacci on this one; mjd says the hands must cross on the hour, but they actually co-incide in the sixty minutes following each hour. The meeting after eleven o'clock takes place on the stroke of twelve, and the hands co-incide rather than cross.

[mjd]

Yes you're both right, I was wrong it is 10

[pquinlan]

I think you were right first time, mjd.

The question doesn't say you start at midnight, so to avoid coincide-versus-cross confusion, start at a time when hands are separate, say 3.30 which is the time as I type. Then the hands will cross eleven times, at (approx) 4.22, 5.27, 6.33, 7.33, 8.44, 9.49, 10.55, 12.00, 1.05, 2.11 and 3.16.

N'est pas?

[Otleybard]

Good point. Looks like everybody's right, but 10's right more often!

[Otleybard]

Sorry, I meant eleven's right more often.

[pandabear]

The keyword in the clue appears to be CROSSED:


As the clock ticks round ... HANDS only CROSS ONCE in every hour

So, in a 12 hour period .... The hands will cross ELEVEN times ... since the hands do NOT cross -

EITHER - at the start (if you start with the hands together)

OR - (if you do not start with the hands together) at the end (where the hands draw up to the starting time but do NOT cross, since the 12 hours is up!