## A Hidden Triple From Hidden Logic

Hidden pairs are rare, but hidden subsets of n > 2 are rarer still. This updated solution of Royle 17-13727, a puzzle from a large collection of puzzles of 17 givens, was an example in The Hidden Logic of Sudoku by Denis Berthier. The solution was posted November 2016 in a review of this book, and is updated here to illustrate another way that hidden subsets can arise. The update was needed because the original post was before 4-fills were normally used in Sysudoku Basic.

Here is the grid of Royle 17-13727 after the bypass creates and resolves two 4-fills, placing two naked pairs in the East box.

Follow the basic trace to see how useful the 4-fills are.

A very unpromising line marking is cut short on the second line, a 5-fill.

At that point, row 1 and column 7 demonstrate four values 3, 4, 7, and 9 in four cells of the NE box, a naked quad. The 3 NE free cells remaining must place 5, 6 and 8.

It’s a hidden triple, in that no candidates of other values can be added to those three cells in line marking. The triple confines 7 to r1, a boxline bringing NW4.

Here’s the grid a few steps into the collapse. The box slinks created along the way are included in the trace, marked with “m”.  A follow up preserving every option requires care to avoid treating a line as fully marked when it is not.

Sysudoku will soon be in page mode. In this mode, weekly posting of new puzzles is suspended. The home page will be a changing report on current updates and offer a brief guide to site features and navigation options. Permanent updating Sysudoku pages will be in The Guide, the About page, and other menu items. Over 500 posted posts will remain accessible by date from the monthly archives, indexed by collection review, title and subject tags. The most recently posted Sudoku will be accessible by simply scrolling back to them.

Weekly posted puzzles will end with several basic level puzzles selected from a series of puzzles that follows the Dave Green Conceptis series in my newspaper, the Akron Beacon Journal. The series is named SUDOKU CREATORS in the ABJ. The puzzles  alternate  with three levels of increasing rank of difficulty labeled as Bronze, Silver and Gold. Those selected for these ending posts are Gold level and compare in difficulty to the 4-star Dave Green puzzles found throughout the blog. I say 4-star, because the CREATORS Golds consistently solve in the bypass without requiring box and line fill stages, as many Dave Green 5-stars do.

To match your basic traces with mine, take maximum advantage of 4-fills, ignoring those that fail to immediately resolve. The first of these appeared In the ABJ March 12, 2022. Writing a trace and listing the 3 and 4 fills is a good way to keep up with their entangled effects.