This post finishes the illustrative review of Frank Longo’s The Nastiest Sudoku Book Ever, with review puzzles 673, 684, 695 and 706. The bv scan and occasional easy coloring continue to be enough for what Frank claimed to be the toughest part of this not so nasty, but entertaining, collection.
Nastiest 673 catches a nasty case of Type4 Unique Rectangle. One of the worst I’ve ever seen.
On the left, the 3-slink prevents any UR partner 4 from its corners, bringing in two more bv.
In the middle, the 5-slink throws out the only two 6’s in c4 outside of the N box, for a boxline removing two more.
Then as the dust settles, another UR emerges, obviously requiring the presence of 9r1c8. I include the magic top hat nice loop that I thought would be important, but now it only marks the raging path of the collapse.
See a doctor about that nasty UR infection, Frank.
Out of line marking, Nastiest 684 only needs 7r7c8 to prevent an extended unique rectangle and collapse the puzzle.
Nastiest 695 followed the recipe closely. An X-wing in line marking, and a definitely obvious Single Alternate Sue de Coq.
A regular 485-wing triggers a boxline for two more removals.
Then an XY ANL and the review’s only finned fish with a fin box removal.
When a large bv field brings out the crayons, two clusters are laid out. Two blue candidates land in the same cell, and get their clan ejected. Green then implies red and 695 is history.
On the battle field, you can see it all from here.
The party ends with Nastiest 706 with two Single Alternate Sue de Coq’s archived. A 259 wing enables . . .
. . . an XY chain ANL (black)to remove 1’s. A 12-wing (purple)removes 9r3c7, but not before another victim sees a wing of the 12-wing by forcing chain(red) through it. The collapse follows promptly.
From this pre- selected set of puzzles from Frank Longo’s The Nastiest Sudoku Book Ever , its fair to say that the book falls a bit short of the title.
However, that’s what we have come to expect from Frank, a ringmaster of the Sudoku circus. At least all of the reviewed nasties get into advanced technique, and with entertaining results, and basic solving is not difficult. This may be just what you want.
Next post, I return to the bent N-set methods to revisit the remarkable BARN, and tell how it was constructed by the equally remarkable StrmCkr, from timber cut by the Sudoku sage, Andrew Stuart.
Systematic Sudoku 
Puzzle 706 is not a proper puzzle, it has two different solutions. Cells 51 & 56 are 2 or 6, Cells 71 &77 are 6 or 9, cells 91 & 97 are 2 or 9.
Puzzle 705 is also not unique, Cells 82, 88, 92, 98 are all 6 or 9
Puzzle 137 is also not unique, Cells 63, 64, 83, 84 are all 3 or 9
Duane, I reworked Nastiest 706 to be sure, but it actually has a single solution. In the comment, I think you meant r5c1 and r5c6 with 2 or 6, r8c1 and r8c6 with 6 or 9, and r9c1 and r9c6. This is interchanging 706 solution values to find another placed grid that meets Sudoku rules and matches the givens, but not another solution to 706. See the difference? The fact is, this alternative placement cannot be logically derived from the 706 givens, because they do arrive inexorably to the solution.
That doesn’t mean that a computer code in a solver cannot find multiple interchange “solutions”. Such codes generally use extreme trial and error, traversing a gigantic tree of trial solutions instead of logical steps. An exception is Andrew Stuart’s rule based Sudowiki solver. It runs through a repertoire of coded logical methods, and gives up when none work. But then if you ask for a count of solutions, Sudowiki reverts to the tree search code and can find some.