3
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Complete the following sequence with just one number:

$$4;\ 9;\ 1;\ 6;\ 2;\ ??$$

Hints

  • It's a real number

  • The sequence ends with that number

  • There could be literally infinite similar sequences with the same ending number

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8
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Could be:

Zero

Get it?

Alphabetically: Four, Nine, One, Six, Two, Zero
Even the complete alphabetical list of all integers ends with Zero

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  • $\begingroup$ Great! Exactly!! $\endgroup$ – Henry Jan 31 '16 at 10:07
5
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The answer is:

5

Because:

49, 16 and 25 are all perfect squares.
And that's where it ends.
And there are literally an infinite number of sequences of squares ending in 5.

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  • 3
    $\begingroup$ or maybe the reason is 4 is a perfect square, so is 9, so is 16 , so is 25. All I mean to say is it might not be 49 according to OP $\endgroup$ – manshu Jan 31 '16 at 7:07
  • $\begingroup$ Not a bad answer but nope! What if the sequence were been "41, 9, 1, 16, 12, ?? Your reasoning would fail ^^ $\endgroup$ – Henry Jan 31 '16 at 10:09
1
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7

I guess because,

4 + 5 = 9
1 + 5 = 6
2 + 5 = 7

i.e. a consistent difference of 5 between every pair of terms

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  • 1
    $\begingroup$ Interesting line of thought. To the downvoters, maybe a comment as to why you feel the need to DV this answer? It is as valid as any other correct answer, and if anything, just proves that the original question is too broad! $\endgroup$ – Phylyp May 22 '18 at 12:01
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    $\begingroup$ Perhaps because the puzzle's assertion that "The sequence ends with that number" is not true of the proposed rule here, for which the sequence could be extended ad infinitum. (@Phylyp) $\endgroup$ – Rubio May 23 '18 at 13:26

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