It is in puzzle #160:
- Code: Select all
1.....9..
...6.4.8.
.4..3...2
..6.8....
.3...57..
9..2...1.
..7..6...
.2....5..
8..1....3
1.....9.....6.4.8..4..3...2..6.8.....3...57..9..2...1...7..6....2....5..8..1....3 # NoFish160 r5c8<>6
SER=7.3
When only whips[1] and oddagons are activated, CSP-Rules finds the same Odagon as Tarek, but also two more, including a 2-digit one of length 11.
Notice that the second oddagon[5] is made possible by the elimination of the oddagon[11]: r8c9 ≠ 6; this amounts to deleting c9 from its second cell: r8n6 and making it bivalue modulo its target (n6r1c8).
- Code: Select all
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = O
*** using CLIPS 6.32-r764
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1.....9.....6.4.8..4..3...2..6.8.....3...57..9..2...1...7..6....2....5..8..1....3 # NoFish160 r5c8<>6
208 candidates, 1220 csp-links and 1220 links. Density = 5.67%
oddagon[5]: r1n6{c2 c9},c9n6{r1 r8},r8n6{c9 c1},c1n6{r8 r3},b1n6{r3c1 r1c2} ==> r5c8 ≠ 6
oddagon[11]: r3n1{c6 c7},r3c7{n1 n6},c7n6{r3 r6},b6n6{r6c7 r6c9},c9n6{r6 r8},r8c9{n6 n1},r8n1{c9 c3},c3n1{r8 r5},r5n1{c3 c5},b5n1{r5c5 r4c6},c6n1{r4 r3} ==> r8c9 ≠ 6
oddagon[5]: c8n6{r1 r8},r8n6{c8 c1},c1n6{r8 r3},r3n6{c1 c7},b3n6{r3c7 r1c8} ==> r1c8 ≠ 6
I looked for the simplest set of rules that could solve this puzzle, so as not to destroy the oddagons. It is bivalue-chains. (Typed-bivalue-chains are not enough.) Unfortunately, they destroy the 3 oddagons, much before they have any chance to appear. In particular, the oddagon[11] elimination is obtained by a mere bivalue-chain[5]:
Hidden Text: Show
After scanning the whole collection, my initial enthusiasm for (fully super-symmetric) oddagons is shaken. I found very few interesting examples where a resolution theory is strong enough to solve the puzzle but not strong enough to destroy all the potential oddagons.
Notice also that there is more in the Obi-Wahn+Tarek collection than the fully super-symmetric oddagons I've coded in CSP-Rules. I don't find all the eliminations mentioned in the file. I don't know exactly what Tarek calls NoFish. My version of oddagons doesn't include any sub-patterns other than 2D-cells (CSP-Variables) that are bivalue modulo the target.