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The strange clock (Posted on 2004-02-17) Difficulty: 3 of 5
I have a very strange clock. At first glance, it looks like a normal clock with three hands and the numbers 1 through 12 all around. The only differences are that the hands are indistinguishable from each other and they are faster. One hand completes a circle in 3 minutes, another in 4 minutes, and the last in 6 minutes. They all go clockwise.

One morning, when I looked at the clock, the hands were all pointing exactly at the numbers 1, 2, and 3.
Later that day, I saw that the three hands were pointing exactly at 6, 10, and 11.

Can you identify which hands I saw each time? Prove it.

  Submitted by Tristan    
Rating: 2.6667 (6 votes)
Solution: (Hide)
I will call the hands A, B, and C, from fastest to slowest. So A goes around in 3 minutes, B in 4, and C in 6.

This puzzle only deals with integer minutes, because all hands point directly at numbers only every minute.

Hand B has only three possibilities. It could have moved from 1 to 10, 2 to 11, or 3 to 6. The number of minutes it takes mod 4 is 1 or 3.

Hand C, in that time could have moved 2,6, or 10 numbers over in that time. The only possibility left considering this is from 1 to 11.

Hand B is left only with the possibility of 3 to 6, and hand A goes from 2 to 10.

So this is what happened:
Hand A went from 2 to 10,
Hand B went from 3 to 6,
Hand C went from 1 to 11,
The time this took mod 12 is 5.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionYeppersJohn2004-02-24 23:59:07
SolutionSolutionsherif2004-02-23 18:51:19
I think me knows it!Mitch Mullings2004-02-22 19:59:31
Solutioni think i got it :)evan2004-02-21 03:08:57
Solutionunique solutionpierre2004-02-19 14:44:58
re(3): SolutionCharlie2004-02-18 15:31:10
re(2): SolutionMital2004-02-18 13:12:58
re: SolutionSilverKnight2004-02-18 12:59:10
SolutionMital2004-02-18 12:57:35
Solutionmy solution -no calculatorsAdy TZIDON2004-02-18 03:49:37
SolutionSolutionGabe2004-02-17 13:03:22
SolutionsolutionCharlie2004-02-17 11:46:54
SolutionWengel2004-02-17 10:54:36
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