Help and advice on solving 'Hard' sudoku

The Game Room
1

I’ve got back into Sudoku after some time away. Most of the puzzles I had been solving were too easy, requiring little more than a couple of scans of all the columns, rows, and boxes. I had figured out how to use naked pairs and naked triples.

Well, now, I’ve got a volume called ‘Hard Sudoku’, presented by Will Shortz, and I need some help on the question of hidden pairs and hidden triples.

Consider the following column, top to bottom. Real numbers in bold, pencilled numbers in square brackets - 8, [2, 3, 5, 7] 9, 1, [2, 3], 4, [3, 5], 6, [3, 5, 7] .

So, does that mean there are two hidden pairs of 2 +3, and a square of 5 followed by a square of 7? Or, does it mean that there are three hidden triples of 3, 5, 7; 3, 5; and 3, 5, 7?

I just don’t think I have fully grasped the concept of hidden pairs and hidden triples, but I sense this is a concept I’m going to need in order to solve the remaining 167 puzzles in this book.

Any advice gratefully accepted!

2

I don’t see a hidden pair or a hidden triplet in your example. A hidden pair would be if you had something like [2356] [2346] [56] [456] [45] The first two squares collectively cover the 2 and the 3, since those are the only squares where 2 or 3 can appear, so nothing else can be in those squares, so change the pencil marks to
[23] [23] [56] [456] [45]

Hidden pairs/triplets generally come with a “non-hidden” pair/triplet (can’t remember the official name) In the example above, in this case, 456 are obviously all covered by the last three squares, so the first two squares can’t be 456, also giving you [23] [23] [56] [456] [45]

For me personally, I am better at discovering the non-hidden pair/triplet/quartet/quintet than the hidden pair!

ETA, naked pair! LOL,it’s in your OP.

3

I’m no expert by any means and I don’t know how hard your “Hard Sudoku” is, but I have reasonable success by only penciling in candidates that can go in two positions. In your example I would only have the 7s and 2s pencilled, nothing else (that said, I also work only in blocks to begin with so I wouldn’t be penciling a column like that anyway). This makes finding “hidden pairs” trivial because none of the other numbers are pencilled. Once I’ve exhausted the options only penciling pairs I start with the triples and eventually, if I have to, I pencil in everything and try to see what else I can find.

I like these guys on YouTube. In this one he demonstrates the technique of only penciling candidates that can only go in two places. https://www.youtube.com/watch?v=IFHOtse62Jo&ab_channel=CrackingTheCryptic

4

My favorite video from those guys is this one, where the puzzle starts with only one (one!) digit populated.

Insane stuff. Way beyond me but fun to watch.

5

This site here - https://www.sudokuwiki.org/sudoku.htm is quite amazing. Import your starting Sudoku and run the steps - it will show all the solving elements at every step. Great way to learn the basics, and maybe some advanced techniques.

I do the NY Times hard version every day, and have never required anything beyond a hidden pair. So that version isn’t particularly hard I guess.

6

But also with more constraints in the rules. Hard to say how interesting it is without knowing those other constraints.

7

Just back for the day - thank you for some interesting links to follow through on. This is the site that I’ve been working from - List of Sudoku Solving Techniques Worth Mastering - Mastering Sudoku , which gets into some fairly complex techniques such as x-wings and y-wings. I’m afraid I’m just not quite getting the logic in hidden pairs and hidden triples yet…

8

Hidden pairs are just pairs, ie two cells that can only have two possible numbers between them, but on first look they have other possibilities as well. Those possibilities can be discounted because the numbers that form the pair do not appear as possibilities in the rest of the block/row/column and so it can only be the pair that fills the two cells. The same concept applies to a hidden triple.

In the example you gave, the 2/3 aren’t a pair because the 3 is a candidate in more than just the two squares with the 2, and the 3/5/7 aren’t a triple because the 3 appears in more than three squares.

9

…and I just proved you right the hard way, by going ahead and making that into two pairs. I was within 6 squares of finishing the puzzle when I had a column with two 7s.

Oh, well, that’s why I’ve started doing these in pencil! I’m going to erase everything and come back at it once I’ve gone through the links/videos that y’all have posted.