This post follows the systematic dismantling of review puzzle SuperTough volume 5, book 8, #5, as it demonstrates the crushing logical power of Medusa coloring. This completes the Sysudoku review of the excellent Super Tough collection found on http://krazydad.com.
3f: c7. 4f: r3, r8. 5f: r2, c3, c8. 6f:r9. 7f:r1.
Close: c1, c2, c9.
I found no SdC , APE or XYZ wings, but the XY curve network revealed . . .
a nice loop XY-chain (blue). Every pair of adjacent candidates in a nice loop is a toxic set, and six 3-candidates left for the coast at the very sight of this one. Another small XY ANL in red removes a 6-candidate.
The new bv bring no bonus profits, and the X-panel comes up dry, so its on to coloring.
The nice loop also makes up the base for a large blue/green cluster, and we get the first color trap right away. It’s a not so obvious trap in r1. The victim 1-candidate is so unfortunate as to be seen by a green 1-candidate, while in the same cell with a blue candidate. Blue or green, it has to clean out its desk and leave the premises.
This departure only extends the blue/green cluster by one cell, but there are plenty of slinks and bv left for another cluster. I can even start one which shares numbers with the first cluster. I’m immediately rewarded with some decisive bridging logic.
Cell r9c8 and the c8 1-candidates assert A: not (blue and orange) => green or red.
Four candidates see both green and red, and resign immediately. And there is more.
In c1 green and red 1-candidates see each other, invoking another toxic color pairing. The logic is:
B: not(green and red) => blue or orange.
No candidates fall into this trap, but combining this with assertion A brings about a merger of the clusters, because
by A: orange => not red => green and by B: red =>not orange =>blue.
Similarly, by B: green => not blue => orange and by A: blue => not green =>red,
so orange is green and red is blue. Mergeration!
not (blue and aqua) = green or tan.
Cell r1c3 shows
not (green and aqua) = blue or tan.
This is a color wrap, because, distributively speaking,
(green or tan) and (blue or tan) => (green or blue) and tan => (absolute certainty) and tan => tan already!
Green and tan forces multiple 2’s in c9 and the SE box, so the true colors must be tan and blue, with very little marking left to reach a color coded solution.
To conclude, I can say that I am amazed at the logical trophies of advanced solving in this very small sample of the Super Tough collection. The puzzles are wonderful for sysudokie sleuthing. Based on my review sample , the Super Toughs grade a notch more advanced than Longo’s Absolutely Nasty Level 4 on the Systematic Sudoku Order of Battle. Both are great collections.
The sysudokie homework is the box marking of puzzle 12 from Paul’s Mastering Sudoku Week by Week. This puzzle provides insight into Paul’s approach to basic solving.