10
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Can you find the last number of this sequence; it may require a bit of a leap?

20, 21, 21, 22, 12, ?

Hint 1:

"a bit of a leap" is a hint to what the sequence of numbers is based on, and doesn't refer to an actual leap in sequential numbers.

Hint 2:

This number sequence is based on a series of numbers, which almost everyone is very familiar with. There's even a popular rhyme about it.

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22
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It's

12

and they're related to

the number of days in each month of a leap year: 29+2=31 (January), 29+0=29 (February), etc. The last two digits correspond to November (29+1=30) and December (29+2=31).

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  • $\begingroup$ Well done :D. I should have probably added in better hints from the start. $\endgroup$ – Tarius Mar 18 '18 at 15:05
16
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The last number is

1202

And so the sequence is

20 21 21 22 12 1202

Because

The digits of the number sequence form a palindrome. The large gap between 12 and 1202 is what is referred to by "it may require a bit of a leap."

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  • 2
    $\begingroup$ Good answer, but unfortunately it's incorrect. The pattern becoming a palindrome is purely coincidental, and in fact adding the two digits to the end of the sequence would also impact the initial numbers as well. Well done though, for seeing the hints at the start, however you may want to rethink what "it may require a bit of a leap" means. $\endgroup$ – Tarius Mar 18 '18 at 11:10
6
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Series would be

20,21,21,22,12,13. Next number is increasing by one simply.

Potential clarification offered by Tarius.

I think @Kriti is splitting the sequence up into three component parts: 20,21 ; 21,22 ; 12,13, where the second number of each part is the increase of the first respectively.

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  • 3
    $\begingroup$ Please explain why you think this is the case... $\endgroup$ – Beastly Gerbil Mar 18 '18 at 21:56
  • $\begingroup$ But 22 increased by one isn't 12? $\endgroup$ – Rand al'Thor Mar 18 '18 at 22:00
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    $\begingroup$ I think @Kriti is splitting the sequence up into three component parts: 20,21 ; 21,22 ; 12,13, where the second number of each part is the increase of the first respectively. $\endgroup$ – Tarius Mar 18 '18 at 22:39
1
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The rule for 20, 21, 21, 22, 12, 21... is:

First figure in each number is the number of different digits of the previous issue.
The second digit is the number of twos in the previous issue.

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  • 1
    $\begingroup$ The second 2 in 22 doesn't play by the rule for the second digit, does it? The previous number is 21, which has a single 2. $\endgroup$ – Phylyp Mar 19 '18 at 4:34

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