Is it possible for a deadlock to occur in Necklace? Can there be a square on which neither Red nor Blue can place a stone?

If it is possible, I need to see an example of that.

If a deadlock is not possible, I need proof of that. Necklace rule sheet

Necklace rule sheet

  • $\begingroup$ Why the downvotes? Too hard for you? 😅 $\endgroup$ Commented Mar 31 at 9:09

1 Answer 1


Can there be a square on which neither Red nor Blue can place a stone?

Yes. If you look at fig.3, neither player can play on the green dot.

But actually no. The only way to deadlock by the crosscut rule alone would be to surround a square on all four sides. This is disallowed by the edge rule. If you consider some contiguous group of squares you can assign them all a value based on their distance from any edge. The square with the highest value will never violate the edge rule. Once has been played on the next closest square is now freed from the edge rule (if it wasn't already). We can continue this until the entire group has been played on since there will always be a square freed from the edge rule, and as previously stated we can't deadlock from only the crosscut rule.

  • $\begingroup$ Good answer. Thanks. $\endgroup$ Commented Mar 31 at 14:57

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