Clock One
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A flea jumps clockwise around a clock starting at 12. The flea first jumps one number to 1, then two numbers t?
A flea jumps clockwise around a clock starting at 12. The flea first jumps one number to 1, then two numbers to 3, then three to 6, then two to 8, then one to 9, then two, then three, etc. What number does the flea land on at his 2008th jump?
please explain how. thank you
Well, in a single rotation of the tick (1, 2, 3, 2), it travels 8 numbers. In 2008 jumps, it makes 502 rotations exactly. This means that after 2008 jumps, it travels 4,016 numbers (502*8). It makes 334 full rotations around the entire clock (4016/12), with a remainder of 8. Therefore, the tick finally comes to rest at 8.
The fact that 2008 is a multiple of 8 is not relevant to solving this problem.
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