## Recent Changes to the iPad App "Sudoku Fundamentals"

Programs which generate, solve, and analyze Sudoku puzzles

### Recent Changes to the iPad App "Sudoku Fundamentals"

- - - - - - - - - - - - - - - - - - - - - - Version 2.4 - 11/20/17 - - - - - - - - - - - - - - - - - - - - - -

Replacement of the Basic Library:

Most of the Basic library puzzles have been replaced, so that all three Basic levels can now be solved without making notes of possible solutions.

The following two images show the Basic range. Underneath each are statistics of what the Grader needed to do and what it needed to find in order to solve the puzzle.

Basic 1 and 3 star.png (66.87 KiB) Viewed 2520 times

All puzzles are solved by first finding unit singles, followed by finding naked singles when all except 2 or 3 empty cells remain in the unit. These unit singles are reported by the Grader as either block singles or line singles (row or column singles) that it found by looking at intersections by the other two units.

These are called “unit” instead of “hidden” singles, because they represent the single possible solution found in a unit, which may be a naked single.

At the 1-star level, only block unit singles detection is necessary, and naked singles were looked for only when 2 empty cells remain in the unit. These naked singles are very easily found in 1-star puzzles; note the number (nSings) of them found by the Grader versus the unit singles (blkSings).

In the 3-star puzzle, the Grader needed to find several line singles, with many more unit checks needed to solve the puzzle.

The last Grader statistic (maxNSeq) is the longest sequence of naked singles found. This is made as small as possible, so that finding naked singles is distributed more evenly. This rewards one during the solution process, rather than finding these singles all in a clump at the end of the solution.

The first three puzzles in the Basic library are 1-, 2-, and 3-star puzzles that include the two puzzles displayed here.

The Grader statistics give you a general idea of what to expect in a puzzle. Find out what you like (or don’t like) by looking at them after you solve a puzzle, not only for these library puzzles, but also for puzzles you have Imported, or copied from newspapers using the Create action. Then when you use the Random action to create your own puzzles, you have an idea of what to specify and which puzzle to Select or avoid when they are displayed by Create’s Random action .

Rewrite of the Basic Topic:

In line with the above, the first topic in the Fundamentals, “Rows and Columns Crossing Blocks” has been rewritten with the new Sudoku puzzle solver in mind. An interactive display lets the user solve an example that includes all the basic strategies, showing how they relate to the rules of Sudoku. And for more fun, the user also learns how to “preselect” a solution in the keypad for entering in multiple cells (particularly useful for Basic puzzles).

New Export Option:

When solving a puzzle, the user is now given an option to export the input puzzle. The user might choose this option to send the 81-character string to someone, or to import it and use its pattern to Create a puzzle using that pattern.

If the user has turned off the option that allows libraries to be updated when the App is updated (implying that the user is doing the updating), then when a puzzle is imported, an action is provided allowing the user to add the puzzle to its library. Since the puzzle might have been one exported from that library, the add is not allowed and the user gets a message instead if a duplicate is found in the library.

- - - - - - - - - - - - - - - - - - - - - - About Sudoku Fundamentals - - - - - - - - - - - - - - - - - - - - - -

The description of Sudoku Fundamentals in the App store gives you a full description of this App along with screenshots.

But the following may be of particular interest to viewers of this forum:

You can copy the textual image of a puzzle in the Puzzles forum board and then use the Import action to display the puzzle. You have to use the iPad copy mechanism to do this, but you can be pretty sloppy. You can start the copy anywhere before the puzzle as long as there are no numbers or periods in the selected area before you get to the puzzle. You can continue the select anywhere beyond the puzzle. Import will extract the first 81 numbers and periods from the selected text (or less if there are less than 81).

The Import action will send this string to the solver. If a valid puzzle, it will then send it to the grader (which will tell you the strategy level and star level). If the puzzle is not valid (or even if it is valid and you select a cell in the puzzle grid) you will see the Create screen which allows you to edit the puzzle.

The Import action also gives you a "Create Protect Pattern" button You can then Clear the puzzle and you have a pattern that you can use to create other puzzles.
nedBlake
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### Re: Recent Changes to the iPad App "Sudoku Fundamentals"

This App had a major update on 11/21/17, and the referenced post was edited a few days later.

The update consisted of an almost total replacement of the Basic library. These puzzles can all now be solved without using notes of possible solutions.

I was not thinking only of Sudoku solver beginners, but also the many solvers that prefer this level of puzzle. And believe it or not, I can now see now why they do after solving many of them myself.

This was a big change for me, who originally wrote this App thinking that the ability to draw an implication chain with your finger on an iPad screen would make it popular. I now get the feeling that chains give most Sudoku solvers a headache.

I am beginning to see why solving Basic Sudoku’s is addictive, and I feel some of this addiction myself. I don’t feel that solving these puzzles is necessarily easy. I won’t admit how long it took me to solve the heart-shaped puzzle in the referenced post, but I know it was probably a lot longer than the person I sometimes see in a waiting room going through a book of Sudoku puzzles would take to solve it.

Anyway, I think these puzzles compare well against puzzles I copied and solved from local newspapers, at least when you compare their relative grader statistics.
nedBlake
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Location: New Bern, North Caroline

### Re: Recent Changes to the iPad App "Sudoku Fundamentals"

- - - - - - - - - - - - - - - - - - - - - -Version 2.5 - Newspaper Mode Added - 8/15/81 - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

This forum thread is now the Support URL for this app. The Apple Store "What's New" refers to the example given here so this post and the app submission have to happen at the same time. But (hopefully) it should be only a few days before release 2.5 gets reviewed and shows up in the store.

"Newspaper Mode" option:

If this new option is selected, the solutions possible in each empty cell are not given to you. Previously, without this option, you were given these solutions for all levels higher than Basic whether you wanted them or not.

This option can be set from the main Menu, since it affects just about every action in the Menu, including which puzzle you are given to solve, how puzzles are created, and how puzzles are graded.

The example below shows how you would solve a puzzle in this mode, following exactly the same steps used by the Grader. It really is a Moderate puzzle, despite its strategy rating of "Advanced" due to its one use of a Y-Wing.

Change in Moderate strategies and visual aids:

Line-Block Intersections are now considered Moderate strategies. The existing visual aid that lets you highlight a particular possible solution is now available at this level.

The visual aid that highlights all cells containing a pair now lets you show only pair cells that can be seen and that have a possible in common with a selected pair cell. This makes a Y-Wing a lot easier to find.

Creation of puzzles improved:

Creation is now done in batches. You are a shown the puzzle and its Grader statistics of the best of a batch while the next batch of puzzles is being created. This also seems to result in a wider variety of puzzles.

If you haven't created a pattern for creating puzzles, you will now be given a default pattern. Try this with the "No Target" option - this will produce puzzles restricted to this pattern for several different levels.

About Y-Wings and using the new visual aid:

You are not likely to see a Y-Wing in a newspaper puzzle. If you are not familiar with them, the following is all you need to know:

A Y-Wing consists of 3 cells, each containing a pair of possibles (perhaps "V-Wing" would have been a better name). It is simple, but very powerful, as it creates a strong logical connection between 2 possible solutions. These possibles can't even "see" each other, and can be located anywhere in the puzzle, which is what makes Y-Wings difficult to see.

A Y-Wing looks like (c,a)--(a,b)--(b,c), where the two "a"s are connected in one unit (row, column or block) and the two "b"s are connected in another unit.

If you look at a Y-Wing as a simple chain, it has alternating strong and weak links, just like many chains do.

If you assume "c" in the first cell is not a solution, then "a" has to be a solution because pairs in a cell are strongly linked: one possible not being a solution implies the other one must be.

The unit connecting the two "a"s need only provide a weak link. No matter how many "a"s there are in that unit, the first "a" being a solution implies the next "a" in the chain is not a solution. The same is true for the "b"s and their unit.

And so forth to the other "c" at the other end of the chain, which then turns out to be a solution. The same is true traveling backwards from the "c" in the last cell to the "c" in the first cell.

And so the two "c"s are strongly linked by implication: one "c" not being a solution implies the other "c" is a solution.

And so any other "c" in the puzzle that can "see" (is in the same unit as) both of these linked "c"s can be removed, as it no longer is a possible solution.

A Y-Wing is a natural for Newspaper Mode, since you don't need to know any other possibles other than the 3 cell possible pairs and the target possible.

The "Show Pairs" visual aid makes Y-Wings more visible. Selecting the middle (a,b) cell will highlight only pair-cells containing "a" or "b" in units containing (a,b).

You do need to ignore the common case where all 3 cells are in the same unit. This would be a naked triple and should be looked at as one, and most likely has already been looked at.

If you used Create in NewsPaper Mode to create a bunch of Advanced one-star puzzles, many of them would contain a Y-Wing.

- - - - - - - - - - - - - - - - - - - - - - - - - Newspaper Mode Example - - - - - - - - - - - - - - - - - - - - - - - - - - -

At the top of the Menu screen below, you will see an option to select Newspaper Mode or not. This new option can be selected here since it affects all the actions in the menu. "Newspaper mode" means that the solutions possible in each empty cell are not given to you - something that use to be true only at the Basic level, but now is available as an option for all levels.

In Newspaper mode, you will find that you go about solving puzzles in a different way, and many find this way more enjoyable. Many really don't want a computer to partially solve the puzzle for them, and then have to look at 50 to 60 cells filled with possible solutions, which either may not be all that helpful, or may be too helpful

The visual aids remain the same, except that "Show Pairs" has been enhanced as shown in the last screenshot. This enhancement makes finding Y-Wings and some other chains a lot easier.

menu + input.png (109.32 KiB) Viewed 1924 times

The following screenshots were made while solving this puzzle following the same steps used by the Grader (which solves a puzzle in the way it assumes a human would solve it).

The first time you select a puzzle from the release 2.5 "Advanced" library, indicate one "star" and you will get the puzzle shown below. You can then also follow the steps used by the Grader.

The Grader solves puzzles in a different way when Newspaper Mode is active. It keeps track of the possibles that might be noted by a user solving the puzzle, and applies strategies based only on what the user sees, just as the user would.

The possibles shown below are all these possibles. At the Basic level, you might not make notes of all of them as the Grader does here. At this level, only units with 2 or 3 empty cells have their cells filled in order to find "easy" singles.

basic + moderate + advanced.png (247.3 KiB) Viewed 1924 times

Basic Level:

The screenshot on the left shows the situation after the Grader realizes it can't solve the puzzle at the Basic level. The Grader got to this point by finding just block unit singles - it wasn't necessary to look for the more difficult to see row or column singles.

Only units having 2 or 3 empty cells were filled with possibles in order to find "easy" singles. What you see here are the possibles left over after almost 11 singles were found that way

Moderate Level:

At the Moderate level, the Grader first looked for naked pairs, triples and quads, but found none that eliminated possibles. The one naked pair (noted as "np:1" in the Grader statistics) was found after the Y-Wing was found. But it did find 4 line-block intersections (noted as "int:4").

If you look at the Fundamentals topic titled "Line-Block Intersection", you will see "Pointing Pair" and "Box-Line Reduction" in the subtitle, which may be more familiar to you. But it is the property of the 3-cell intersection, where a line (row or column) crosses a block that is behind both of these strategies.

If you tap "Selected Possible" and then tap possible "9" in the keypad, you will circle all "9"s. In this case we get to see examples of both the above strategies.

In the top left block, you will see two 9's in the intersection with row 1, and none elsewhere in the block. This means that the solution must be in the intersection, and so the other 9 in row 1 can be deleted. You can delete it without getting out of "Select Possible" mode, since 9 is the selected possible and so tapping it in the keypad acts normally.

This is an example of a "Pointing Pair", and it often is a pair but it doesn't have to be one.

When the Grader sees a possible in more than one 3-cell intersection in a block, it sees if it can find the intersection where the possible doesn't show up elsewhere in the intersecting row or column. This is the case in the block below, where column 3 intersects with the block. In this case the two other 9's in the block can be deleted.

The only difference between "Pointing Pair" and "Box-Line Reduction" is whether the block or line determine that the solution is in the intersection. Once that is determined, all other possible instances outside the intersection in either unit can be deleted since the intersection is part of both units.

For similar reasons, the top row 3's in the top left block can be removed, and the leftmost 6 in row 6 can be removed.

If a puzzle is not solved at the Moderate level, it is likely that all possibles will be filled. At this level, the Grader adds possibles where they look useful, such as when a naked multiple already exists in a unit, but some cells are still empty.

But the number of possibles that you have to deal with is minimal compared to non-newspaper mode.

At this level, you will find the "Show Pairs" visual aid useful as well as "Selected Possible". "Show Pairs" colors the background of all cells containg a pair of possibles.

In this release this aid has been improved as follows: when you select a cell containg a pair from all the shown pairs, only those cells in units to which the selected cell belongs that contain exactly one of the selected cell's possibles are colored.

In looking for a Y-Wing, you would select a pair cell as the possible "middle" cell of a Y-Wing, for instance the (6,9) cell shown. (We borrowed the Draw mode from the Extreme toolkit just to show you the Y-Wing, not that it was at all necessary to draw it.)

You can see that there is a (6,5) and a (6,3) as possible end cells, but only (6,5) has a corresponding (9,5) as the other end of the Y-Wing.

So 5's are the Y-Wing end-possibles. One of these 5's has to be a solution, which means that the 5 in row 3 column 1 can be removed, since it "sees" both of them.

This exposes the naked pair (3,6) in column 1, which exposes the now naked 9 in the top cell, and then it's singles to the end.
nedBlake
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Location: New Bern, North Caroline

### Re: Recent Changes to the iPad App "Sudoku Fundamentals"

I have run into a problem with the App store.

Apparently, the Apple development tool that I use (Xcode) needs to be updated, and I discovered that I need to update the OS on my Mac before I can I can do that.

I expect their will be problems.

I will let you know when Version 2.5 is available in the store with a post here -

Sorry,
Ned
nedBlake
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Posts: 36
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Location: New Bern, North Caroline

### Re: Recent Changes to the iPad App "Sudoku Fundamentals"

Suduku Fundamentals 2.5 now available in App Store (see 8/15 post)

Managed to get High Sierra OS installed on my MacMini, but it took a couple of hours.

Price is now \$1.99
nedBlake
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Posts: 36
Joined: 08 May 2016
Location: New Bern, North Caroline