This week in Sudoku - a Triple, triple, triple solution!

For almost the last twenty years I have been a Sudoku addict. Even if I look at nothing else in the paper, I have to solve the Sudoku. I have a Sudoku desk calendar. People give me sudoku books, which I rapidly solve all the way through and move on. When Boston’s subway system had its Metro papers, with two or three Sudoku puzzles, my goal was to solve them all before I got to my stop.

A bit of terminology here – apparently (according to Wikipedia) a 3 x 3 square set aside by bold lines within the 9 x 9 Sudoku square is a block. A set of three blocks in a horizontal row is a band, and a set of three blocks in a vertical row is a stack.

Over the years I began to notice patterns. One of these is that in any 3 x 3 “block” within the 9 x 9 puzzles, you would frequently find cases where the same two numbers appeared in horizontal rows in every band. (but not the same horizontal rows, of course, since each number can only appear once in each 9-cell row in the 9 x 9 puzzle) And if the same two numbers appeared in one row in each block, you would find that two other numbers would be repeated in a different horizontal row in every band, and, if you looked, two other numbers would be repeated in the third row of each block in that band. In other words, if two digits were repeated in every horizontal row of a band, then every horizontal row in that band would have repeated pairs of digits. The same thing holds true for vertical rows in stacks in Sudoku puzzles.

It’s not required. I’ve done plenty of puzzles without such repetitions. And it might be only on some bands and stacks. It can occur in both bands and stacks in a puzzle.

If there’s a name for this, I haven’t yet encountered it.

More rarely, you have a similar situation with all three numbers in a horizontal row in every block in a band being identical. If this is the case, then every horizontal row in that band will have a horizontal row with the same digits in every block in that band. Again, if one set of three cells in a horizontal row is repeated in every block in the band, then they all will be. And the same thing goes for every vertical row in a vertical stack. (Note that the repeated cells might not be in the same order).

Again, not every band or stack must obey this. Often only one band or stack displays this behavior, although more than one might, and it might be bands and stacks that can show it.

Again, I haven’t found recognition that this occurs, or a name for it. Although I’m sure I’m not the only person to notice this.

This morning, while solving the Sudoku puzzles in this week’s Hippo (New Hampshire’s weekly free newspaper, reminiscent of Boston’s PhoenixGive flowers! — 02/09/23 ) I noticed a Grand Slam in their Sudoku puzzles. As in many papers, the Hippo gives you three Sudoku puzzles - an easy, a medium, and a hard level of difficulty. Of course, I have to solve all of them.

I was amazed to see that one of the puzzles had something I’d never seen – all three Bands were cases of 3 repeated digits in each horizontal row. Not only that, but every Stack was a case of three repeated horizontal rows. Every Band and every Stack showed the same pattern.

But it was even better than that. When I looked more closely at each of the three puzzles, I saw that every single puzzle had that same feature. Each had every Stack and every Band showing sets of three repeated digits in every block. .A triple Grand Slam!

And it’s in the Valentine week issue. It’s a Valentine’s gift to Sudoku freaks.

(Main Hippo Website – https://hippopress.com/ )

Nice! I think you’ve described it quite well, but can you post a picture of the solved puzzles, just because?

Well, my copy’s all marked up, and I got the last one.

So as not to deprive you of the opportunity to solve them yourselves, here they are:

Easy

.1…B…B…7…6…5…8…3…2
.B…8…3…B…4…B…B…6…5
.B…B…B…8…B…2…9…B…B
.4…B…9…B…7…B…2…8…B
.3…2…8…B…9…B…B…B…B
.6…5…B…B…B…3…B…9…4
.B…4…B…B…5…B…B…2…B
.B…B…2…B…B…9…6…B…B
.7…B…5…3…B…8…B…1…9

The "B"s are blanks. I tried putting underscores in there, but the bulletin board simply eliminated them, making things look confusing

Medium

.4…B…9…5…6…B…1…B…3
.B…5…B…B…2…B…B…B…B
.3…B…B…7…B…B…5…B…B
.B…6…B…B…B…B…B…4…7
.B…B…B…9…B…7…B…B…B
.B…9…B…B…8…B…B…3…1
.2…3…1…B…7…B…B…B…6
.B…4…B…B…5…B…B…1…B
.6…B…B…3…1…B…B…B…9

Hard

.B…5…3…B…B…B…8…B…B
.B…2…B…B…1…8…B…B…B
.B…B…B…B…B…B…B…2…4
.B…B…4…B…6…B…7…B…B
.6…B…B…3…B…B…B…B…2
.B…B…B…B…B…4…1…8…B
.8…1…6…7…3…B…B…B…B
.B…7…B…B…9…B…B…B…B…
.B…B…B…B…B…B…5…7…B

There you go. Recopy into 9 X 9 grids with blanks where the "B"s are and have at it!

I had no clue what you was on about until I did the 3 sudokus - Thanks for taking up at least 2 hours of my valueless time.
Now I understand : )

Sudoku has become a favourite pastime for me over the last year or so - I’m addicted to the “Cracking the Cryptic” YouTube channel. If you are not familiar, they post multiple videos of Sudoko solves every day with links to the puzzle so you can try em yourself. Recommend.

If I’m understanding the OP’s description correctly, the phenomena is sometimes called “striping”.

I second Cracking the Cryptic as the best sudoku on the internets.

If “striping” is indeed a name people use for the situation where all three blocks in a horizontal or vertical row have the same three numbers in every horizontal/vertical line, then one usually has a puzzle with no stripes. It’s a little less uncommon to have one stripe. I have seen cases with two or even three stripes, but when there are three of them I had never seen all three be vertical, or all three horizontal. It would be two one way and the third perpendicular to that. So I was astonished to find in this case that all three “stripes” were horizontal – something I had never seen before. But then I further saw all three vertical stacks were "stripes, as well, which seemed far more amazing. And then I noticed that all three puzzles had three vertical and three horizontal stripes, which was truly fantastic! I don’t think the three puzzles — Easy, Medium, and Hard, were isomorphic. (That is, you couldn’t create one of the other puzzles by substituting different numbers in the same places, or by rotating or reflecting the puzzle grid, or doing both. The three puzzles were unique solutions with six stripes).

Really amazing. I doubt if most people properly appreciated it.