It's not intuitively clear to me how the game can go on forever -- I would expect that, eventually, you would hit upon some valid pattern. The explanation in the text didn't really make sense to me. Could anyone help with this?
The game could use a better definition of what constitutes a pattern.
> A pattern is a sequence of pebbles repeated three times in a row.
By that logic, player 2 would have lost at their fifth turn. ... And 'in a row' is open to interpretation since it is additional information to 'repeated three times'.
I think it's pretty clear that a string s of pebbles is a pattern iff there exist strings x and y such that s = x|y|y|y, where | denotes string concatenation and y is nonempty.
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It's not intuitively clear to me how the game can go on forever -- I would expect that, eventually, you would hit upon some valid pattern. The explanation in the text didn't really make sense to me. Could anyone help with this?
The game could use a better definition of what constitutes a pattern.
By that logic, player 2 would have lost at their fifth turn. ... And 'in a row' is open to interpretation since it is additional information to 'repeated three times'.
I think it's pretty clear that a string s of pebbles is a pattern iff there exist strings x and y such that s = x|y|y|y, where | denotes string concatenation and y is nonempty.
EDIT: Clarify that only y is nonempty.
I was confused also. My guess was that maybe a “sequence” has to be 4 or more pebbles?