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.
If you take the hands of each at 1, 2 and 3 and put them 5 normal minutes ahead, you get the answer. Allow me to explain. The hand on the 1 will be the hand to take 6 minutes for a full circle. In one normal minute, it takes 10 seconds or 2 numbers ahead to make the equivalent. It goes from 1, to 3, to 5, to 7, to 9 and finally to 11. The numbers just said are taken from every 1 normal minute. The hand on the 2 will be the hand to take 3 minutes to complete a full cycle. In 1 normal minute, it takes 20 seconds or 4 numbers ahead to make the equivalent. It goes from 2, to 6, to 10, to 2, to 6, and then to 10. Finally, The hand on the 3 will be the hand to take 4 minutes to complete a cycle. In 1 normal minute, it takes 15 seconds or 3 numbers ahead to make the equivalent. It goes from 3, to 6, to 9, to 12, to 3, and finally to 6. Pretty good, eh? I'll try to solve more! Ta-ta for now!