# Next number in sequence, understand the 1st mistake to avoid the 2nd

31 30 31 30 31 31 30 31 30 31 31 __ ?

Some of you said the 10th number would be 21, not 31. Almost all of you were aware of this wrong answer, even if you knew it was ridiculous!

Some of you will now say there are two possibilities for the 12th number. Wrong! Learn from the previous mistake.

The sequence consists of

numbers of days in month, starting with March

Some of you said the 10th number would be 21, because

it was said the world would end on Dec 21, 2012

28 - number of days in February 2013 (not a leap year)

• Joe's answer is more detailed, but I accpeted this since it has the important elements, and was first according to timestamp. Commented Oct 24, 2016 at 19:01
• did anyone still actually remembers the date of that Maya calendar (what is Maya?) thing? Commented Oct 24, 2016 at 20:46

Props to FrodCube for the first part of the work on this - go upvote him.

The sequence, and the next number in it are

28 - the sequence is the number of days in each month, starting in March 2012 and moving forwards

The first mistake is that

many people thought the world would end on December 21st 2012.

"Almost all of you were aware of this wrong answer" - it was widely known.
"even if you knew it was ridiculous" - even if you didn't believe it was true.

Because of the first mistake, we then know that

We're specifically talking about December 2012 for month 10. The following February was 2013 which is not a leap year, so we know that the next number is 28 and not 29.

• Dam, how could I miss that... I searched the whole history of Dec 21 on internet and didn't find that. Commented Oct 24, 2016 at 11:45
• "go upvote him": I see no evidence of FrodCube's gender. Commented Oct 25, 2016 at 7:20

Quick guess

28

because

It's just the list of days in a month starting from march

but to be honest I have no idea about the mistake.

• Really, how many days are in February? Commented Oct 24, 2016 at 8:07
• @deepthought, 28/29 depends Commented Oct 24, 2016 at 8:10
• Then there would be two possiblities for the 12th number. Which is what I expected some of you would say... Commented Oct 24, 2016 at 8:13
• I totally forgot about February having 29 days... Commented Oct 24, 2016 at 8:31
• December 21st is the winter solstice - the shortest day of the year. I don't see how that's relevant right now, but the number matches up so I'm mentioning it :) Also you could argue that February should be 28.25 since the leap year is just to catch up the missed quarter days, so maybe there's something related to the winter solstice there?
– Joe
Commented Oct 24, 2016 at 11:26

Is it:

30

because the sequence is just:

31 30 31 30 31 repeating itself [i.e. 31 30 31 30 31 / 31 30 31 30 31 / 31 (30?)]

This seems to be too simple...

• There's two "31 31" in the sequence. It's not repeating Commented Oct 24, 2016 at 8:30
• In his reasoning , there is two "31" cause the end of the sequence is equal to the beginning. [31 30 31 30 31][31 30 31 30 31][31 _ ...] Commented Oct 24, 2016 at 8:31
• Why on earth did so many people think 21 for the 10th number... Commented Oct 24, 2016 at 8:35
• @deepthought: I don't understand your "21" reference. Please explain? Commented Oct 24, 2016 at 10:54
• @deepthought: Yes, I understand now, it was just that you replied with a hint, but it wasn't really indicated that it was a hint, so I interpretated it as a direct question to the solution that was proposed and it made little sense to me. Commented Oct 25, 2016 at 8:31

Could it be

31

This is why:

Breaking up the sequence into smaller blocks: 31 30 31 30
31 31
30 31 30 31
31 31

• I dont understand your reasoning Commented Oct 24, 2016 at 8:37
• I think quarkle simply breaks it into a block sequence where the two blocks are "31 30 31 30" and "31 31". First it starts with block A, then block B, then block A, then block B, where A is "31 30 31 30" and B is "31 31". That would fulfil the original sequence. Commented Oct 24, 2016 at 10:58
• Welcome to PSE! Commented Oct 24, 2016 at 11:35
• Yes, its like RickardNi explained, except the second block A is slightly different. So more like block A block B block C block B. Commented Oct 24, 2016 at 12:59

Is it

30

Because

Repeating sequence seems to be -1 +1 -1 +1 0

I am going to assume that the mistakes were made by the people who have answered this question already and I say the answer is

31

because

since there are 12 numbers, it would be convenient to repeat the sequence exactly twice. So the first six numbers, 31, 30, 31, 30, 31, 31 should make up the sequence, as of quarkle's answer, however, I believe this answer would make more sense because instead of two 'blocks', there is one single sequence.

This way there is only one possibility for the 12th number, but I have no doubt someone will tell me I'm completely wrong.