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Can you fill in the missing numbers of these number sequences?

_, 3, _, 9, _, 14, _, _, 21, 27, _, 35, _

_, 7, _, 15, _, 22, _, 30

_, _, 5, 7, _, _, 12

The three sequences may or may not be linked together in some way. If you can come up with the missing numbers, please provide an explanation.

I have tried to solve this for about a week now and I've gotten nowhere, hopefully someone here comes up with something.

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2 Answers 2

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As a starting point, I think the bottom sequence is

1, 3, 5, 7, 8, 10, 12

which is

the calendar month numbers of months having 31 days.

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    $\begingroup$ There are 12 months in a year, and the last sequence ends with a 12. The second sequence ends with a 30, which could indicate days (days of a month), and the first sequence has the possibility to end with 52 which could indicate weeks of a year. Just an idea, I haven't gotten anywhere with it. $\endgroup$
    – user265554
    Commented Feb 22, 2016 at 20:05
  • $\begingroup$ @user265554, me neither. :-) $\endgroup$
    – Hellion
    Commented Feb 22, 2016 at 20:33
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After I checked at least 1000 calendar systems (perceived), I have still no clue about the first two lines. But now I have good knowledge in things I never need again... i.e. 8-day-weeks :-/

Something productive now: The same sequence by Hellion also exists if you imagine a piano keyboard and start with the F-key as 1. The white keys are the numbers then. Maybe the others are something with guitar chords or so?

On the other hand, the 52 as the scale for the first line mentioned by user265554 is very exceptional. 21, 27, ..., 35 should end in 40 or maybe 41 / 42.

And now I suspend myself till google is able to solve this in 20 years.

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