This is a question from an IQ test (NSE test designed by Ivan Ivec and Theodosis Prousalis). The link for this test is https://free.ultimaiq.net/nse.htm
The sequence is:
120, 10, 3, ?, ?
The answer is:
120, 10, 3, 1, 1
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2$\begingroup$ Deducing any pattern from three data points is impossible, unless the sequence is very famous. $\endgroup$– BassJul 8 at 14:14
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1$\begingroup$ @Bass exactly. But fortunately for us we have 5 data points, which makes it less impossible ;) $\endgroup$– LezzupJul 8 at 16:16
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2$\begingroup$ oeis.org/search?q=1%2C1%2C3%2C10%2C120 $\endgroup$– Marco13Jul 8 at 22:17
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$\begingroup$ Is there an answer key somewhere? $\endgroup$– eyeballfrogJul 9 at 17:17
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1 Answer
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Here is one possible explanation:
every number is the square root of the previous number, and then round down to the nearest integer.
$ x_{n+1} = \left\lfloor\sqrt{x_n}\right\rfloor $
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$\begingroup$ That formula makes no sense, unless you meant to use $x_{n+1}$ and $x_n$ instead of $n+1$ and $n$. $\endgroup$ Jul 8 at 19:03
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1$\begingroup$ @JaapScherphuis, ah, silly me. Of course I meant that. msh210, thanks for the edit $\endgroup$– LezzupJul 8 at 19:47
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$\begingroup$ This function is specifically crafted, using without any limitation any possible mathematical operations, to fit five given data points. It's an uninteresting overfit. Also, there is absolutely no way that this function could have been inferred from the three first data points that were given in the exam question, so it isn't the intended solution either. $\endgroup$– BassJul 9 at 22:03
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3$\begingroup$ @Bass The question is, ostensibly, from an IQ exam. Pardon my cynicism, but I find that a lot of questions from those kinds of exams rely on massive overfitting. $\endgroup$ Jul 10 at 4:29