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I think I have solved this one, but I've got 2 different solutions.

$$1,2,3,-1,3,2,1,x,x$$


First solution (I think this is the right one)

I just noticed a pattern where the numbers between the 1s just alternate like this: we have the first one made by 1 then 2, 3 and -1 ---> 1, 2, 3, -1.
Then we should alternate 2, 3 and it becomes -1, 3, 2, 1.
And then we have the $x, x$. Considering that it always alternates we can just write 2,3 instead of x.So we get something like this:

$1,2,3,-1,3,2,1,2,3$


Second solution

I just think the number ones are what you should add to the numbers.

Example We have 1 at the beginning. 1+1=2 and 2+1=3
Then we have to rewrite 3, and do 3-1=2, then 2-1=1.
Then we should replace the x with 2 and then 2+1=3 so it would be something like this:

$1,2,3,-1,3,2,1,2,3$

Can you confirm one of these theories or come up with a better solution?

Source:http://zagaza.ru/za548.htm

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  • $\begingroup$ Can't see any difference between your two solutions (apart fom the narrative which I can't follow for #2). $\endgroup$ – Weather Vane Jan 6 at 23:43
  • $\begingroup$ You basically see the 1 and the -1 as something that you should add,let's say at the beginning we see 1,then you should add 1 everytime till there's another 1 in this case 1,2,3,-1,3,2,1,x,x we have 1 at the beginning then 2, 2+1=3,then there's -1 and the sequence stops,now we should add -1,we have to rewrite 3 and then do 3+ -1= 2 and here we have -1,3,2 now there's 1,we just rewrite 2(last number of last sequence) and add 1 because it's positive so 2+1=3 and there we have 1,2,3,-1,3,2,1,2,3 $\endgroup$ – alnesi Jan 7 at 1:38
  • $\begingroup$ i'm still trying to figure out if those solutions are correct $\endgroup$ – alnesi Jan 7 at 1:41
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I can't read the question in the source so its hard to tell what they're going for - I feel like something like a $+, -, \times$ pattern could fit, however there is an issue with sign on the $\times$ so maybe $\times(-)$
So starting with 1 and 2, we add: $1+2=3$.
Then we subtract: $2-3=-1$
Then we multiply and negate: $3\times(-)-1=3$
Now start the pattern over:
Add: $-1+3=2$
Subtract: $3-2=1$
Multiply and negate: $2\times(-)1=-2$
Add: $1+(-2)=-1$

Giving $1,2,3,-1,3,2,1,-2,-1$

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  • $\begingroup$ yea in this test you also need to find a clever answer,i thin your solution it's right? do you have any social network contact or even discord,steam etc where i can contact you? $\endgroup$ – alnesi Jan 9 at 23:59
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I had a look at some of the other puzzles on the link and I don't think that all of them are necessarily a 'real sequence' but rather require a clever answer. So here is mine:

The sequence starts with $1, 2, 3$ and then follows $-1$ after which we have the same numbers going in reverse order $3, 2, 1$. So, my guess is that only numbers 1, 2, and 3 are used further, with 1 or -1 indicating the order in which they follow, which leads to the following:
$1, 2, 3, -1, 3, 2, 1, -1, 1, 2, 3, -1, 3, 2, 1, -1$ or possibly
$1, 2, 3, -1, 3, 2, 1, 1, 1, 2, 3, -1, 3, 2, 1, 1$

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