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There was this sequence on a magazine and the reader has to find the next number:

10, 2, 4, 6, 2, 8

I couldn't find one, then I found the answer in the next magazine. They say the number is 5, so the sequence is

10, 2, 4, 6, 2, 8, 5

Now I know the answer, but I can't find the logic behind it.

Why is this the answer?

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    $\begingroup$ Nothing on OEIS $\endgroup$ – Fabich Jul 26 '16 at 9:17
  • $\begingroup$ The pattern -8, +2, +2, -4, +6, -3 and the Numbers converted to letters J, B, D, F, B, H, E So no outright pattern, however I tend to find the pattern for things like these are -X then +X but the 5 at the end seems to throw that off $\endgroup$ – Mr.Burns Jul 26 '16 at 10:35
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    $\begingroup$ @Revenor Number Sequence can have a lot explanations, for example there is (almost) always a polynomial answer. Can you provide more information : - What magazine is it ? - Is there any context ? - Is there any other examples of sequences/puzzles in this magazine so we can understand there logic ? $\endgroup$ – Fabich Jul 26 '16 at 12:49
  • $\begingroup$ I am not the reader of this magazine. It's something about a friend that reply me this sequence. I suppose is some sort of puzzle magazine for casual readers, so i suppose it should be a simple answer, but i can't find any logic. $\endgroup$ – Revenor Jul 27 '16 at 8:42
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    $\begingroup$ @Revenor What if your friend randomly chose some numbers and asked you to figure out a sequence for these numbers? $\endgroup$ – Bradman175 Aug 10 '16 at 0:14
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Are we sure the following number is $5$, and not :

$2$ ?

Because :

It could be three nested sequences :
$A = 10, 6, 2, ...$ or $a_n = a_{n-1} - 4$ with $a_0 = 10 $
$B = 2, 2, 2, ...$ or $b_n = 2, \forall n$
$C = 4, 8, 12, ...$ or $c_n = c_{n-1} + 4$ with $c_0 = 4 $

The sequence would be:

$a_0 = 10, b_0 = 2, c_0 = 4, a_1 = 6, b_1 = 2, c_1 = 8$

Then, the following numbers would be :

$a_2 = 2, b_2 = 2, c_2 = 12$

Or :

I can be utterly wrong and this is more lateral-thinking than I thought!

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I tried it! Might be the correct answer or a vague logic

10,2,4,6,2,8

10,2 On dividing 10 from x leaves remainder 2 Min Number: 4

10,2,4 On dividing 10 from x leaves remainder 4 Min Number 6

10,2,4,6 On dividing 10 from x leaves remainder 6

Some smartness here, modified the clause

On dividing 102 from x leaves remainder 6 Min Number 12

10,2,4,6,2 (because 12 => 2)

On dividing 102 from x leaves remainder 12 Min number 18

10,2,4,6,2,8

Quotient in this case was 5

So may be that is why answer is 5.

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    $\begingroup$ Thanks for the attempt, but changing the rule in the middle of the sequence like that (twice!) should never be the intended answer to a sequence puzzle. $\endgroup$ – bmcfluff Jul 28 '16 at 23:00
  • $\begingroup$ @bmcfluff, you got any leads? $\endgroup$ – th3pirat3 Jul 29 '16 at 5:22
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10, 2, 4, 6, 8, 5

10 / 2 = 5, the end number is the common multiple of the previous number divided by the initial number

The common multiple becomes the second number

The common multiple is added to the second number 3 times to make the following three numbers in sequence

Then topped off by the 5 resulted from the common multiple divided from the initial.

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    $\begingroup$ It is not an explanation it is more of expressing the pattern behind it, so I already will acknowledge it is not a good answer. $\endgroup$ – user22047 Aug 6 '16 at 15:39
  • $\begingroup$ I think you've missed a number 2 before 8.. You've explained well in your perspective but even a number being missing... $\endgroup$ – Ram Visagan Aug 9 '16 at 4:53

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