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Today, I was in Rome for a vacation. The most peculiar thing happened. A gnome walked up to me. Uttering no words, it handed me a slip of paper.

0, 1, 1, 2, 3, 2, 5, 5, 5, 9, 4, ?

Naturally, I was confused. I tried to solve it, but I couldn't. What number is ??


The gnome came up to me again, after I had spent considerable effort on the problem, and had gotten nowhere. It handed me this note (hint):

              Hi
             Weird
           Isn't it?
           Try harder
     You'll get it, I'm sure
 Keep traveling this road; observe

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  • $\begingroup$ I know of a sequence that closely matches this one, although slightly different. Is the third term here definitely correct? $\endgroup$
    – hexomino
    Jan 27, 2023 at 14:12
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    $\begingroup$ @hexomino Yes, it definitely is. $\endgroup$ Jan 27, 2023 at 14:32

1 Answer 1

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Had the gnome walked all the way from Pisa, by any chance?

The sequence seems to be counting

the number of individual straight pen strokes needed to write the numbers of the Fibonacci sequence in Roman numerals.

Like so

 0, 1, 1,  2,   3, 2,    5,    5,   5,     9,  4, ?
  , I, I, II, III, V, VIII, XIII, XXI, XXXIV, LV, ?

If this is the case, then the next number would be

11, corresponding to the number of straight pen strokes needed to write LXXXIX.

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  • 2
    $\begingroup$ Ah, I was way off, +1 $\endgroup$
    – hexomino
    Jan 27, 2023 at 22:27

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