Quantum Examples in August 10 Tough

The Tough Sudoku of August 10, 2009 contains an excellent example of the power of using Quantums. This particular advanced Sudoku has the added bonus of utiliyzing a MUG, which is a type of Uniqueness deduction. These are rather advanced sudoku solving strategies, tips or tricks.

If this is your first visit to this blog, welcome! Unfortunately, if you are a first time visitor, this page may seem like it is written in a different language. Well, it is!! Previous blog pages may be helpful. Links to these pages are found to the right, under Sudoku Techniques. The earliest posts are at the bottom, and if you have never perused the intricacies of our special coded language here, you may wish to start close to beginning. The list is rather large, so below find a list of links that may be pertinent to this particular puzzle.

• Locked Candidates
• Pairs Triples Quads
• Forbidding Chains 101 The Theory
• Forbidding Chains 102 The Practice
• Advanced Forbidding Chains, Forbidding chains are now referred to as Alternating Inference Chains (AIC)
• Unique Rectangles
• Tough Puzzle solution for August 7, 2009, a less complex introduction to Quantums
• Quantum Examples in August 8, 2009 Tough
• Definitions: This page has been recently updated, finally

Although this page may contain a complete solution path, the main intent of this page is to illustrate the use of Quantums in solving Sudoku.

The Puzzle

For those whom do wish to view a full solution path, I have posted at the bottom of this page a group of steps sufficient to slay this puzzle. I may also post an alternative path, which is almost as interesting as this one, but does not use Uniqueness.

An Almost Quantum Naked Pair

An Almost MUG

Below, note that candidates (16) are almost locked into b123, e123, i123. If they were locked into those 9 cells, nothing could occur in the puzzle to avoid an eventual Unique Loop. This is not difficult to prove.

It is clear, therefor, that at least one item circled in green below must be true.

Again, note the (16) at e1. One could write that as a result of that cell, we have the following SIS:

• [(6)b7, (6)g23, (QNP16)e1f2]

A Quantum Kraken used in a complex AIC

Below, note

• Circled in green is the MUG SIS.
• Circled in yellow is the Almost Quantum Naked Pair(16) e145.f4
• Two additional Native sis are noted, shown as black lines.
  1. (6)h57
  2. (6)efg4
• Four Native weak links are noted, shown as red lines.

One can now write, with relative ease, the following complex AIC: below, *'s denote the MUG SIS

• (QNP16*)e1f2 = [(6*)g23 = (6*)b7 - (6)h7 = (6)h5] - (6)g4 = (6)ef4 - (6)f5 = (QNP16)e145.f4
• => e23≠16

Of course, one could have instead used the Almost Hidden Pair 16 at ef4:

• (QNP16*)e1f2 = [(6*)g23 = (6*)b7 - (6)h7 = (6)h5] - (6)g4 = (HP16)ef4 - (345)e4 = (NP16)e14
• => e23≠16

The puzzle now quickly falls apart.

A Possible Solution Path using the Quantums listed above

Of course one can solve this puzzle without using the steps indicated above. Below is one way to solve it using them:

• 1) Start 23 UP 24
• 2) (LC2)ab5 => defhi5≠2, UP 30
• 3a) Given (MUG 16)bei123,
  • (QNP16)e1f2 = [(6)g23 = (6)b7 - (6)h7 = (6)h5] - (6)g4 = (6)ef4 - (6)f5 = (QNP16)e145.f4
  • => e23≠16
• 3b) (NP34)de3 => ef2, abc3≠34, UP 81

SIS Specrtrum:

• Total SIS: 13
• Max Depth: 10
• non-ssts steps: 1

Below, another path that does not use Uniqueness, but does use: a very pretty wrap around chain, or cont. AIC loop plus a Quantum SIS derived from a potential gaurdian loop 34 (Impossible pentagon) at c34, d35,e4.

• 1) Start 23 UP 24
• 2) (LC2)ab5 => defhi5≠2, UP 30
• 3a) (5=6)g4 - (6=8)g2 - g6 = e6 - d5 = (8-5)d8 = (5)d45 => e4≠5
• 3b) (5)d4 = (NP34)cd4 - (34)e4 = (NP16)e14 - (16)e3 = (NP34)de3 - (34=7)c3 - (7=8)c8 - (8=5)d8 loop =>
  • d5≠5, f4≠4, e25≠16, ab3≠34, c7≠7, ei8≠8
• 3c) Given impossible pentagon (34) at c34, d35, e4 => Quantum SIS[(16)e4, (7)c3, (8)d5]
  • Note chain in 3b has done almost all the work:
  • (8*)d5=[(7*)c3=(NP16*)e14 - (16)e3 = (NP34)de3 - (34=7)c3] - (7=8)c8 => d8≠8, UP 81

SIS Spectrum for alternate path:

• Total SIS: 23, but much overlap of sets used in the same fashion multiple times
• Max Depth: 9
• non-ssts steps: 3

Below, yet another alternate path:

• 1) Start 23 UP 24
• 2) (LC2)ab5 => defhi5≠2, UP 30
• 3) Given complex gaurdian loop:
  • abd5, c34,d3 =>
  • Quantum gaurdian sis[(7)c3=(58)d5] =>
  • (5*)d5 = [(8*)d5 = (7*)c3 - (7=8)c8] - (8)d8 = (8)d5 - (8)e6 = (8)g6 - (8=6)g2 - (6=5)g4
  • => de4<>5, UP 32
• 4a) (HP16)ef4 => ef5≠6, (np16)ef4
• 4b) (NP16)e14 => e23≠16, UP 33
• 5) (NP34)de3 =>abc3, ef2 ≠34, UP 81

SIS Spectrum for second alternate path

• Total SIS: 17
• Max Depth: 11
• non-ssts steps: 1

DigressionThis puzzle is not that difficult that it requires such advanced techniques. Often, at Sudoku.com.au, the tough puzzles do not rise to the difficulty level that one can reliably illustrate the more complex ideas. Thus, I have decided to occasionally slay the mice with elephant guns.

In the second alternate path, if one wishes to, one can append steps 4a, 4b, and 5 to step 3. This would result in one large chain => (7)c3. The puzzle is then reduced to singles. (UP 81). The depth of this mega step would be 14. It would look something like this:

• (7*)c3 = [(5=8*)d5 - (8)e6 = (8)g6 - (8=6)g2 - (6=5)g4] - (5)de4 = (5-6)g4 = (HP16)ef4 - (345)e4 = (NP16)e14 - (16)e3 = (NP34)de3 => c3<>34 UP 81