The sense of the meeting is, that the mystery sequence is just a temptation to overthink. Since the sequence goes even, odd, even, odd, even, odd, and there is only one even number in the possible answers on offer, that must be it: 10.
I certainly yielded to the temptation, if that was what it was, trying to tackle the thing via partial differential equations and symplectic field theory.
Given the social context here—a low-level clerical job, not Head Atom-Smasher at Lawrence Livermore or chief AI researcher for Google—I think the simple alternation of even and odd is probably the right answer.
Fellow overthinkers came up with some interesting possibilities, though. A couple:
Given a single digit number, add 5.And:
If the result is a single digit number, add 1.
Repeat until the result is a two digit number.
At that point, subtract 1.
If the result is still a two digit number, subtract 3.
Repeat until the result is a single digit number.
So the answer is 10.
The difference between 2 and 8 is 6.These, I should say, were among the least overthought suggestions. Wilder spirits alphabetized the given sequence to BGHMLI, then transposed those letters left and right looking for actual words, with utter lack of success. But hey, perhaps if we shift to the Hebrew alphabet …
The difference between 7 and 13 is 6.
The difference between 8 and 12 is 4.
The difference between 13 and 9 is 4.
So the difference between 12 and the next number needs to be 2.
So it is either 10 or 14.
Since 14 isn't an option for a solution, I would deduce it is 10.
The friend who sent me the puzzle in my October Diary has pointed out, in reference to my worked solution, that the problem can so "be solved using standard high school real functions that appear on every scientific calculator." I have added a suitable correction at the end there.
And, also in reference to the October worked solution, I got one email from a reader wanting to know the meaning of "wolog." Sorry, it's math-geek-speak: "without loss of generality."