- #71

#### jedishrfu

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42 days in seconds is 42 . 24 . 36 . 100: ##2^8 . 3^4 . 5^2 . 7##

10! is 10 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 which is ##2^8 . 3^4 . 5^2 . 7##

How did you come to learn this arcane factoid?

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In summary, the cheap wall clock from 2017 failed in less than 1 hour, and the new clock with a new battery also failed in the same way at the 41 second position.f

- #71

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42 days in seconds is 42 . 24 . 36 . 100: ##2^8 . 3^4 . 5^2 . 7##

10! is 10 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 which is ##2^8 . 3^4 . 5^2 . 7##

How did you come to learn this arcane factoid?

- #72

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OK, I get this, but...42 days in seconds is 42 . 24 . 36 . 100: ##2^8 . 3^4 . 5^2 . 7##

How do you get this? That doesn't seem to be a shortcut or anything: 256.81.25.710! is 10 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 which is ##2^8 . 3^4 . 5^2 . 7##

- #73

Science Advisor

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I can't remember when I first saw this, but it stuck in my mind as another candidate for the Ultimate Question, "What is the smallest integer number of days that is an exact factorial number of seconds?"How did you come to learn this arcane factoid?

$$\begin{align*}

&\frac

{42 \times 24 \times 60 \times 60}

{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\

&= \frac{60}{10} \times \frac{1}{9} \times \frac{24}{8} \times \frac{42}{7 \times 6} \times \frac{60}{5 \times 4} \times \frac{1}{3 \times 2} \\

&= 6 \times \left( \frac{1}{9} \times 3 \times 1 \times 3 \right) \times \frac{1}{6} \\

&= 1

\end{align*}$$

- #74

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I just prime factored the 10! Factors and counted up the 2s 3s 5s and 7sOK, I get this, but...

How do you get this? That doesn't seem to be a shortcut or anything: 256.81.25.7

2.5.3.3.2.2.2.7.2.3.5.2.2.3.2.1

You can think there are 5 even factors in 10! Hence five 2s But 8 gives you two more and 4 one more for a total of 8 2s or ##2^8## …

- #75

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The standard cure is to put a match stick under the appropriate corner of the clock for which the clockmaker (or repairer) will charge five guineas.

*This, of course, is based on the normal rules of the household i.e. that the clock is wound up on a Sunday evening.

- #76

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- #77

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That'll be five guineas please...So there's your answer @anorlunda : tilt your clock:

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