| | There are four plausible answers which I can see to this question, namely 21, 80, 81, and indeterminable. I would argue that indeterminable would be the best answer, given that there are valid reasons to choose more than one of the other answers.
21 is a plausible answer for the reasons given by Laure and Ciro, which amount to the same relation expressed in different ways.
81 is plausible if one assumes that the sequence is based upon those numerals, in numerical order, which are comprised of the digits 1 and 8 alone, to the exclusion of 0,2,3,4,5,6,7 & 9.
But the algorithm by which I derived the sequence was to list in numerical order those numbers which begin with vowels in their English spelling. Hence, the next number (or, better, word) in the sequence after eighteen is eighty. As of this post, I am the only person (with inside knowledge, obviously!) who chose that answer.
Why did I post this "survey"? I was recently asked my opinion of IQ tests, to which I answered that many so-called intelligence tests have questions with more than one possible answer, and that if one is ingenious enough, one can often outthink the question. I remember specifically a test of this sort given in my high school to which I and about 20% of the respondents gave what was considered a wrong answer. I remember arguing the case and having the results changed.
I have also come across such "brain-twister" questions asking which of the following items does not belong in the list. Typically, four out of five of the items will be verbs, one a noun, four will begin with a consonant, one with a vowel, four will be native English words, one will be a borrowing from French, and so forth, with the "not-belonging" item differing according to each criterion.
I designed this question purposefully to have a non-mathematical criterion, namely English spelling, on the assumption that I would be able to find some other criterion or criteria - and the answers of the poll show that there were two other possible answers, and that epistemologically, only "indeterminable" was truly valid.
My thanks to those who have been willing "test subjects."
Ted Keer
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