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I came downstairs and set my new clock to 12 pm. Its Sunday. I go back to work on Monday. My shift starts at 12pm, in a days time. Unbeknownst to me, the clock is defective.

At 45 seconds into the first minute, the second hand stutters in the same place for two seconds and then continues as normal. It will then happen again, 61 seconds after the second hand continues (where it is 46 seconds past on the clock, though at the time it will be actually 48 seconds past) and will continue like this.

If I just use this clock and no other, how late will I be for work tomorrow?

This puzzle is based on a real clock I found on my desk, stuttering away and
telling me the wrong time.
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    $\begingroup$ It's a trick question; everyone uses their phone to tell time. $\endgroup$ – Ian MacDonald Jan 21 '16 at 20:25
  • $\begingroup$ Ok, what if i'm an old man, who hates mobile phones and modern things? 200 million people don't have a mobile phone. @IanMacDonald $\endgroup$ – Beastly Gerbil Jan 21 '16 at 20:44
  • $\begingroup$ I feel like there are a few more people in the world than that that don't have cell phones. :/ $\endgroup$ – Ian MacDonald Jan 21 '16 at 21:04
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    $\begingroup$ Maybe, I just got it off a website :) $\endgroup$ – Beastly Gerbil Jan 21 '16 at 21:23
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There are $60 \times 60 \times 24 = 86400$ seconds from when you set the clock until you are supposed to be at work. After the first stutter, the clock loses 2 seconds for every 61 seconds that pass.

$(86400 - 45 - 2) / 61 \approx 1415.623$, so the clock will stutter (for 2 seconds) 1415 times (+1 time for the initial occurrence) before you are supposed to start work.

Thus you will be late by

$1416 \times 2 = 2832$ seconds, or 47 minutes, 12 seconds.

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  • $\begingroup$ Nice work! Down to a point $\endgroup$ – Beastly Gerbil Jan 21 '16 at 20:43
  • $\begingroup$ @JoeBeastlyGerbil I just realized that my initial answer was actually off by a factor of 2. I counted each stutter as a single second, when in fact it is 2 seconds. $\endgroup$ – GentlePurpleRain Jan 21 '16 at 22:13
  • $\begingroup$ Oh! I didn't notice! I feel embarrassed now. $\endgroup$ – Beastly Gerbil Jan 22 '16 at 16:18

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