SOLUTION: The minute hand of a clock points directly at the 11. What number will the minute hand point at after 5,555 minutes?

The minute hand takes 5 minutes to point to the next number, so
we divide

  1111
5)5555

So it has pointed to a new number exactly 1111 times in those 5555 minutes.
 
Now every time it has pointed to 12 new numbers it has made a complete
revolution.  So we divide again, this time by 12: 

     92
12)1111
   108
     31
     24
      7

So it has made 92 complete revolutions and ended up with
a remainder of 7 more numbers than those 92 complete
revolutions from where it started, and so it has ended up 7 
numbers past pointing to the 11, and that makes it point to the 
number 6.

Edwin