Discover Rules of Sequence Board Game

[Quixotic]

Post the next step in the sequence:

http://img9.imageshack.us/img9/2796/n36.gif


I'm still working on a solution for this. As far as I see, the problem lies in discovering the rules of a game (I assume it is a game) that would produce such patterns in sequence.

 

[Quixotic]

No replies whatsoever, but I never did figure this one out. Anyone at all want to have a go?

 

[davee123]

No replies whatsoever, but I never did figure this one out. Anyone at all want to have a go?

I played around with it a bit, but I couldn't come up with anything useful. I went under the assumption that it was something similar to "life", but with different rules, but I couldn't find anything relevant with rules involving immediate neighbors. Could be something completely different, though.

DaveE

 

[ƒ(x)]

No replies whatsoever, but I never did figure this one out. Anyone at all want to have a go?

Will you tell us where this came from?

 

[Quixotic]

Will you tell us where this came from?

It comes from one of the many now defunct amateur "IQ tests" online. It's no longer available for that purpose.

 

[Abzu]

My take

http://img107.imageshack.us/img107/2492/abzgame.th.png

 

[Quixotic]

My take

http://img107.imageshack.us/img107/2492/abzgame.th.png

Your method?

 

[TheStatutoryApe]

No replies whatsoever, but I never did figure this one out. Anyone at all want to have a go?

It seems to be a game in particular, which you have hinted at, running backwards. Standard enough looking corner play to deduce that much. I am having a bit of trouble though since I was guessing that the X's represented opposing pieces but the positions of the X's are not consistent while the black dots are. There does not seem to be evidence of any captures either.

 

[Quixotic]

It seems to be a game in particular, which you have hinted at, running backwards. Standard enough looking corner play to deduce that much. I am having a bit of trouble though since I was guessing that the X's represented opposing pieces but the positions of the X's are not consistent while the black dots are. There does not seem to be evidence of any captures either.

To me it looks (visually) most like either a variant on John Conway's "Life" or something like Minesweeper, but, as you say, what we believe to be game pieces don't necessarily behave as such.

 

[TheStatutoryApe]

To me it looks (visually) most like either a variant on John Conway's "Life" or something like Minesweeper, but, as you say, what we believe to be game pieces don't necessarily behave as such.

Ah, I guess then you were not hinting. It looks to me like Go. Particularly it looks like a diagram of corner play except progressing backwards and X's instead of white pieces. The structure makes sense. I can not figure out how to make the progression make sense though.

Oh... I just noticed the pieces are in the boxs instead of on the intersections as they are in Go. Its been too long since I played.

 

[Soca fo so]

Looking at the first two steps, it kind of looks like this could be a variation on checkers with the pieces taking horizontally and vertically instead of diagonally but then I don't immediately see if this could be used to get to the third picture.

I assume this was similar to what you were thinking with your solution Abzu?

 

[DaveC426913]

To me it looks (visually) most like either a variant on John Conway's "Life" or something like Minesweeper,

Now that would be a funny game to write - organisms struggling to survive and multiply in a field of mines!

Maybe you could build some artillery to take down the gliders...

 

[Soca fo so]

Ah now I see, it's a variation on checkers where you can take horizontally, vertically, and diagonally.

 

[Abzu]

I think the players capture each others pieces by jumping over them, any direction. Something in the first 3 turns suggested that the dot is doing the first move every turn. The leftmost dot in the 4th turn was spared by the cross-player because he would have lost in turn 5 had he taken it.

 

[Soca fo so]

Yeah I think you're right. I was thinking that they might only be allowed to take once in each direction per turn.

 

[Quixotic]

I think the players capture each others pieces by jumping over them, any direction. Something in the first 3 turns suggested that the dot is doing the first move every turn. The leftmost dot in the 4th turn was spared by the cross-player because he would have lost in turn 5 had he taken it.

Do you mind annotating the game's moves as you see them?

 

[DaveC426913]

Do you mind annotating the game's moves as you see them?

Well, that would be giving the whole thing away, now wouldn't it? You've been given the key...

 

[Abzu]

Something like this:

http://img43.imageshack.us/img43/415/abzgame2.th.png

 

[DaveC426913]

Something like this:

http://img43.imageshack.us/img43/415/abzgame2.th.png

See now, that's what I call not giving too much away...

 

[Quixotic]

See now, that's what I call not giving too much away...

Considering that the link looks to have 404'd...

 

[DaveC426913]

Considering that the link looks to have 404'd...

Yes.

 

[Quixotic]

Yes.

Steps 3 and 4 are where I'm uncertain about the logic behind the choices I think are being made.

 

[davee123]

The whole checkers theory seems absurdly wrong to me, although it would work. Assuming that you had columns labeled A-F and rows labeled 1-6, then:

Spoiler

From State 1 to State 2:
O jumps from C6 to C4, capturing the X at C5.
X double-jumps from C3 to C1 (capturing C2), to E1 (capturing D1).

From State 2 to State 3:
O triple-jumps from D3 to D1 (capturing D2), to F1 (capturing E1), to D3 (capturing E2).
X quadruple-jumps from A5 to C5 (capturing B5), to C3 (capturing C4), to A3 (capturing B3), to C1 (capturing B2).

It doesn't make sense that it would be the answer, but regardless, even if it's correct, Abzu's answer is wrong:

Spoiler

Note of course that the jump sequence goes from a single jump to a double jump to a triple jump to a quadruple jump. It's possible to extend this pattern and have O make a quintuple jump (eliminating all the X's except for the one at C1), which in turn is followable by a sextuple jump by X, which, no matter how you slice it, seems to end up with an X always at C5, making it the only occupied square on the board.

I still don't like that as an answer, but it does admittedly work.

DaveE