Accelerating Clock

Algebra Level 2

This clock is too fast! Once it is turned on, the second hand will complete 11121\dfrac{1}{12} revolutions in the first minute, 12121\dfrac{2}{12} revolutions in the second minute, 13121\dfrac{3}{12} revolutions in third minute, and so on, continuing in this manner until it is turned off (or otherwise ceases to operate). If the second hand is pointing at the 12 when the clock is turned on, what number will the second hand be pointing at 17 minutes later?

Details and Assumptions:

The second hand moves in a clockwise direction. The clock continues to operate for the full 17 minutes.

Bonus: Where would the second hand be pointing 1 day (24 hours) later?


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