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What three-digit numbers best complete the following sequence:

33, 45, 54, 32, 11, 23, ___?

There are two possible answers. One is composite and one is prime. Find both.

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  • $\begingroup$ Three-digit?... $\endgroup$ – nicael Jun 8 '16 at 16:12
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    $\begingroup$ @nicael Yes, three-digit. $\endgroup$ – user24855 Jun 8 '16 at 16:15
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I think the answers are

$322$ (composite) and $211$ (prime)

Reasoning

If you convert the numbers into musical notes so that $1, 2, 3$ are the 'do', 're', 'mi' of the musical scale, then the sequence with the composite number ending corresponds to the first line of "Ode to Joy" (from Beethoven's $9$th symphony) and the sequence with the prime number ending corresponds to the second line.

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  • $\begingroup$ Nice try. However if you don't get both answers at the same time, that means your answer is probably incorrect. (I should've put it this way :) ) $\endgroup$ – user24855 Jun 8 '16 at 16:41
  • $\begingroup$ Okay, I've had a better idea. $\endgroup$ – hexomino Jun 8 '16 at 16:46
  • $\begingroup$ I've edited my answer to something different. $\endgroup$ – hexomino Jun 8 '16 at 16:53
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    $\begingroup$ Lol, how was it supposed to be easy? Not really obvious. $\endgroup$ – nicael Jun 8 '16 at 16:57
  • $\begingroup$ lol maybe a riddle always seems easy to its author. :P $\endgroup$ – user24855 Jun 8 '16 at 17:23

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