Three Ways to Bypass an ABJ CREATORS


The second Akron Beacon Journal CREATORS of 3/15/22 Sudoku turned out to be a good one for comparing Sysudoku bypass solving without 3,4-fills, with 3-fills only, and with every resolvable 4-fill. Scroll back to see the givens grid above.

My bypass trace without fills,  goes through values 1 through 7 with little follow through. Then the action is in values 8 and 9.

All three comparison traces reach the solution shown later.

Want to spot the hidden dublex Chdx9 that begins the last leg? If you played it out and are into 3-fills, you might have noticed how many you were passing up.

With 3-fills, the solution is reached on one value, 3. It’s interesting how 3 – 9 clues and subsets generated by dublexes and cross hatches are now produced by 3-fills. This shows how 3-fills add  basic solution pathways, and why harder puzzles provide fewer 3-fills.

The 3-fill trace goes on to the final solution.

As you might expect, 4-fills add more pathways to the basic solution. Since 4-fills resolve less frequently, I normally include a 4-fill in the trace only when it immediately resolves. Most of these occur because a missing value sees two or three 4-fill cells in its box. You will probably spot the exceptional case of three cells in separate boxes seeing the same value as you look for the missing value confirming the normal case.

You could do otherwise, but I normally resolve givens 3 and 4 fills before starting the 1 – 9 value list. It’s because n-fill follow up is a more systematic procedure, requiring less searching. Here, as in the all 3-fill case, we don’t get around to that list.

All three traces end with the same candidate combinations that account for the difficulty of the puzzle. The 3-fill trace ends on a 3 value leg, but both the no n-fill and 4-fill end with the same hidden dublex.

My problem with doing 3 and 4-fills exhaustively is overlooking the start of a new one. I’ve lost a lot of time going back to overlooked 3 and 4-fills on blog puzzles to be published. When you this happens in ordinary solving, you very seldom need to go back looking for an extra solution path.  Unless, of course, your oversight is caught by a fellow Sysudokie you compete with by sharing traces.

Coming next in this 4-fill clinic is Akron Beacon Journal Gold CREATORS of 3/30/22. Starting off normally in the values list, a clue revealing a 4-fill is actually a missing value in a 5-fill that resolves to the 4-fill. Actually looking for 5-fills isn’t worth the time.

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The First Beacon Journal Gold


 In the first CREATORS Gold of 3/12/22, a 4-fill created by the third clue begins a long follow up leg through a second 4-fill. A hidden dublex helps on E4. The bypass trace jumps back to continue effects lists four times.

Here’s how it looks at W5, just before several naked pairs are resolved to fill out the solution.

The BJ Gold of 3/12/22 is solved in the bypass with 3-fills only. It looks easier.

This suggests that exhaustive 4-fill analysis be deferred until 3-fills only fails. But even then, there’s no need to pass up the easily spotted placements some 4-fills provide.

Next week, the second Beacon Journal Gold of 3/15/22 falls in the bypass three ways: without 3 or 4-fills, with 3-fills only, and with 4 and 3-fills. I had to go back and correct oversights over and over, so I probably missed a few. Here’s your chance to beat the blog.

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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.

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Sysudoku Basic Subsets in a Sunday 5-Star


In this post, a Dave Green Sunday 5-star illustrates how naked and hidden subsets are spotted in Sysudoku Basic, a 3-stage process to identify candidates, and solve many Sudoku puzzles in the process.    Sysudoku Basic finds clues and subsets while accumulating candidates. Many solvers and most Sudoku literature use the keypad style of representing candidates, and a mechanical process that generates all of the candidates permitted by the given clues before any solving begins .

In this post, a Dave Green Sunday 5-star illustrates how naked and hidden subsets are spotted in Sysudoku Basic, a 3-stage process to identify candidates, and solve many Sudoku puzzles in the process.    Sysudoku Basic finds clues and subsets while accumulating candidates. Many solvers and most Sudoku literature use the keypad style of representing candidates, and a mechanical process that generates all of the candidates permitted by the given clues before any solving begins .

In this post, a Dave Green Sunday 5-star illustrates how naked and hidden subsets are spotted in Sysudoku Basic, a 3-stage process to identify candidates, and solve many Sudoku puzzles in the process.    Sysudoku Basic finds clues and subsets while accumulating candidates. Many solvers and most Sudoku literature use the keypad style of representing candidates, and a mechanical process that generates all of the candidates permitted by the given clues before any solving begins.

The purpose of Sysudoku Basic is to identify clues, subsets and strong links (slinks) and all candidates consistent with them, without generating many candidates that are eliminated before they contribute to solving.

A strong link is a pair of candidates, which includes at least one true candidate. The first stage of Sysudoku Basic is the Bypass, so called because it records on the grid along with clues, only the candidates of subsets. Strong links are recorded in a two further stages, box marking and line marking.

Here is the general definition of a subset:

How can a set of n values in a set of n cells be known to be the solution values? In a naked subset, there are no other values in these n cells. A single candidate of each value must eventually be placed in each cell. Candidates of these values in the line or box outside the subset are removed.

In the hidden subset n values in a box or line are found to be confined to n cells. Each of these cells will eventually claim one of these values, so candidates of other values can be removed from the confining cells.

As to singles, a naked single is a cell with a single value in it.  A hidden single is the only cell in the house with the value in it. The keypad number scanned grid is great for spotting singles. But in Sysudoku Basic, we get a lot farther, while looking for clues, not singles.   Let’s just do the bypass and see how the subsets show up.

Here is the grid after the bypass. Two 4-fills occurred and one was resolved. In the bypass, we’re into clue patterns, not candidate patterns.   Of the 10 clues found, there was one naked single and five hidden singles.

In the keypad grid, see if you can use the candidates to find the naked single and hidden singles. In the bypass, we don’t look for them. It’s not the right time.

As it happens, an advanced technique does begin here, showing how the uncluttered basic grid supports more than basic. As you mark the r6 4-fill, you might notice that C5 and SW5 leave only the same two columns for 5 in r1. That establishes a 5-wing in r1 and r6.

In the bypass trace, we put the 5-fill on the top line. It’s there to account for the 5-wing. Note how a subset pair (a subset with n =2) is marked in the trace.

The red symbols mark the  5-wing in r1 and r6. The wing will remove 5 candidates in c3 and c8, as the rows are marked.  In the bypass and box marking, how are box, row and column slink partner candidates distinguished?

The box marking trace lists the boxes containing a slink for each value. A box slink is exactly two candidates of a value in a box, a strong link. The list includes aligned triples, marked by “t” after the box name. Slinks are listed as effects, when they are caused by another slink.

A hidden pair 56 occurs in r1 above, when 6 is limited, along with 5, to the same two cells in r1. It’s a “hidden” pair because these two cells are reserved for 5 and 6. When r1 is marked, any other candidates, like the number scanned 1, 3 and 7 candidates on the keypad grid above, will be removed.

In line marking, the lines with fewer unfilled cells go first. Filling a line can effect other lines, changing the order. The list starts with 3 and 4 fills, then comes  r1, and a naked triple.

After the ouside 1,3,7 candidates, of the hidden pair 56 are removed,  the naked triple subset becomes obvious. As other rows are marked, no 5 candidates will be added to c3 and c8.

As lines and boxes are covered in line marking, ‘look for subsets as we begin to see all candidates in each line and box. We watch the values smaller in number. Naked subsets are the more obvious.

When we get to r2, the first 6-fill, you probably saw the naked triple 137 as soon as the line was filled. But a hidden is there as well. Let’s consider how to find them, based on this example.

For naked subsets, look for cells containing the same values. For hidden subsets, look for values limited to fewer cells. Here’s a definition designed for finding them.

The keyword is “confined”. We found the r1 hidden pair when we knew 5’s were confined to columns 3 and 8, and we realized that 6 in r1 was confined to the same 2 cells. In r2, we see the two values 2 and 4 in only two cells for a  hidden pair.

There is another hidden triple in r2, but the hidden pair 24 in r23 and r25 eliminates additional candidate 5r23 for the clue NE5, which destroys the 5-wing, but adds two more 5-clues. .We picture subsets by curves surrounding the candidates and diamonds around eliminations.

The collapse :

This post concludes the series of Dave Green Conceptis puzzles illustrating techniques in recent Sysudoku Basic.

We’ll follow with a few basic level puzzles from a new series replacing the Dave Green Conceptis puzzles in my newspaper, the Akron Beacon Journal.

But first, next post is an updated basic solving of Royle 17-13727 earlier posted 11/15/2016. You can look that post up by date by the monthly archive list on the right. The post next week features its 4-fill resolutions and its box hidden triple, and illustrates looking up a puzzle by subject tag.

As to 4-fills, I went back to the KrazyDad Insane review of a very tough collection which was updated before I used 4-fills extensively, to see if 4-fills would make a decisive difference. There was not one resolvable 4-fill in the review.

If you want to look up a collection review in on the monthly archives list, go to the Titles page and slide right onto the collections titles for post titles with monthly archive dates. Try it out. You might be surprised.

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Dave’s Octuplet 


In this post, 3-fills leave a near solution in the bypass, with an entirely blank box. Box marking resolves it systematically.

Seeing the four 5-fills and box corner candidates, you might suspect that this is a follow up on the 4-star of the last post. But really, you should ignore the 5-fills until you’ve rung out the 3-fills.

That goes swiftly with both 3-fills resolved and the bypass ending in a near collapse. Except for the Center box.

The bypass trace shows what it takes to get there.

Box marking does the walls and the C box. Whenever you get slinks of more than a few values in a unit, start counting values and covering cells.  You may spot a subset. Here,  8 values slink into 8 C cells, a naked octuplet.  But that also means 3, the missing value, must be placed in r6c6.

Everything then falls into place.

Next week, we conclude this series of Dave Green basic level Sudoku with the Sunday 5-star of 10/3/21, which illustrates the essential facts about hidden subsets. Try it out beforehand.

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Dave Defies the Bypass on a July Saturday


This post encounters a very odd situation. All the givens in your homework Dave Green Saturday 4-star of 7/18/21 are on corner cells of the boxes. No double line exclusion (dublex) or cross hatch clues in the bypass. The past few posts on 4-fills suggest what you might do with a grid full of 5-fills. Here we’ll solve the 4-star in two ways. After we examine how to use the 5-fills to wring out line slinks, you get to find them all. Then we’ll ignore that anything is different, and carry out normal box and line marking, while exploiting every 4-fill, as in the previous post. Then we’ll see what happens when we start box marking with your line slinks.

Here’s another look at the Saturday 4-star. Values 2, 7 and 9 are missing from r1. Given 3r3c3 bars 3 from r1c12 and 3r6c7 bars a 3rd cell, leaving two cells, and a 3-slink in r1. Similarly, given 9r3c7 and 9r7c1 produce a 9-slink in r1. Going to r3, value 5 is missing and 5r1c4 bars 5 from three cells, for a 5-slink in r3.

Now follow up with 2 missing from r6, 8 and 3 from r4, 6 and 3 from r6, 9, 7, 8 and 5 from r9.  Then do the same for columns. The slinks may produce naked pairs, 4-fills and 3-fills.

Normally you would follow up the naked pairs and their resulting 3-fils immediately. Naked pairs in lines r7, r9, c1, and c3 produce 3-fills, and their resolutions can bring clues to add 4-fills and 3 -fills

This traces the follow up of the naked pairs, bringing . . .

this grid, with several clues, to the bypass

The bypass now closes out the 4-star like a 4-star

Here’s where we leave off tracing.

Next we dip into Friday 4-stars again to see an extreme subset I ran across, an octuplet. That’s  8 cells containing 8 values. Of course there is a complementary subset with one cell containing one value, but you can judge which is easier to spot. This Dave Green hit the Akron Beacon Journal 11/05/2021.

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Doing Every 4-Fill


In the Dave Green 5-star of 1/23/22, four 4-fills are available before starting the bypass values list, on r2, r8, c2, and c8. It brings up the possibility that 4-fills can solve this Conceptis puzzle by themselves? We normally put 4-fills first, but in this unusual case, we’ll try to resolve each new 4-fill as clues and subsets are placed.

The grid after the first four has two of the starting 4-fills resolved.

The trace shows that NW4 from the resolution of the 4th, reduces the 3rd to  a 3-fill, which is immediately resolved.

The fill resolution style collapse is paused only to show how in tracing, effects of the same value as the cause are listed first. For example, here C2 is the newest cause, and the effect list will read (N2, E2, N6). The reason is, that, in posting new effects in PowerPoint, it’s easier to use all the copies of one value before changing to another value.

That effect ordering appears in the final trace, which shows how the 4-fills go all the way.

The box names and values makes it easy, doesn’t it? Now imagine how easy it is to trace down what went wrong, when you find that you departed from the solution on a particular placement. Human engineering

The next Dave Green surprise is a Saturday 4-star that denies the bypass a single clue. You might think that deserves more stars, but it turns that 4 is enough. The post will demonstrate an alternate route to an easier bypass, when a Sudoku composer like Dave pulls this on you.

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4-Fills Lead off on a  Dave Green Surprise


In this Sunday 5-star of June 13, 2021, two 4-fills are resolved before the bypass value march begins. Follow-up continues in box marking, leaving little line marking to be done.  Coloring is demanded and it responds, with an unexpected discovery.

The two 4-fill traces show exactly what happens.

In r1, 4 is missing and can’t fill in NE. In r9, 9 is missing and can’t fill in SW. With 9 placed, 457 are missing, and r1c1 can’t be 4 or 5.

The most important take away is, what signaled these moves?

Then if you follow this bypass trace,

and pass this grid to box marking,

an ordinary box marking turns into something else.

 Coloring the almost filled grid, notice how the removal of 1r8c8 allows the blue/green cluster to be completed.

That means there are at least two solutions. Something that isn’t supposed to happen, but when it does, it can be discovered by coloring. In this case, we don’t really know. I might have gotten a given in the wrong place when I dragged them into my template grid.

I meant it when I said “at least”. For the correct answer, use one of the many backtracking solvers that cover the whole tree of possible solutions. I consulted Andrew Stuart’s on his Sudokuwiki site to learn my possibly mistaken version of the Dave Green puzzle has 5 solutions.

Next time, we look at a Sunday 5-star with four 4-fills on the opening grid. Ordinarily, 4-fills are passed over if they don’t resolve immediately, but in this case, let’s fully process each one and see how we like that experience. It appeared in my paper 1/23/22.

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All the Way With Dave


This post goes through Sysudoku Basic with the Dave Green puzzle published in the Akron Beacon Journal on Sunday October 10, 2021. It’s the first in a series of published Conceptis puzzles selected to illustrate basic moves introduced in the later years of Systematic Sudoku, the blog.  In this series, we pause before many significant moves, to give the trace readers the opportunity to see if the move is in their spotting repertoires, and if they know how and why the move works.

Starting on the bypass, is your first move C1? It takes a dublex in the middle colulmns to limit C1 to c5 and a cross-hatch in box E to limit it to r4. That move shows the satisfying challenge of the bypass. It also shows the value of the uncluttered grid as you pit clues and subsets against clues and subsets.

After (C1, W2, NE3), column c7 is a 4-fill. You respond by checking for missing values seeing more than 1 blank cell. In c7 missing values 2 and 6 both see two. SE6 fails to see a third, but 2 does, placing SE2, and leaving a 3-fill in c7.  NE3 also creates a 4-fill in r3. Will the 3-fill or 4-fill be resolved?

All that action can be recorded in the trace, which handles the bookkeeping, and keeps you apprised of exactly where you are. You read a trace by filling out your own grid as you go.

Tracing the fill of c7, the 3-fill does resolve, and its clue SE5 creates another 4-fill in r7. Two of the four missing values place themselves in separate boxes, leaving two naked pairs in the boxes.

Moving ahead, W3 closing a 2 by 2 square in the West box is the next  significant event.

Line c3 missing the square has value 6, not in the square. That places 6 in r4c12  E4, and a new 4-fill in r4.

Continuing through the bypass, the E box fills in, and two more 4-fills are resolved.

Here is the grid passed on to box marking.

Box marking brings in box slinks, marking them with “pencil marks” along the cell top. For trace readers, only the box need be named for each value. Here the combined marking for 1 and 2 in NE creates a naked pair, reserving two cells for a c8 3-fill, promptly resolved.

Continuing in box marking value by value. The 6 list adds the 6 value to the three unfilled cells of r6. That finishes a wall in the C box, starting a plunging follow up for you to complete and trace.

The grid passed on to line marking incudes another resolved 3-fill in the 7’s.

It’s all on the box marking trace:

Line marking completes the candidate field. Each row or each column is assigned a fill string of digits including all missing candidates on that line. The fill string is copied along the line, and digits seen by clues or subsets are deleted. The remaining candidates are placed in the cell, with slink partners positioned to identify the direction of the slink. Lines are filled in increasing order of free cells, so easier fills come first. The trace records the order of line filling.

Bv are marked and candidates are positioned as each line is filled. When rows or columns are marked , the unfilled lines in the other direction are marked. This is the close and it doesn’t require fill strings.

Here is the line marked grid. Just as the Close is started on c4, a hidden single 7 is discovered in the column being filled. The line marking trace showing the collapse and the solution follow.

The line marking trace on the rows is short here, because so many were already filled. The close finishes line marking on the columns, with the collapse on the first one.

This Sysudoku Basic series of Dave Green puzzles actually started last May 25, 2021 when two  Sunday 5-stars full of 3, 4, and yes, a 5-fill, were posted. You can look them up by post date on the monthly list on the right. That, and the titles page, is a ticket to hundreds of bypass traces.

Next time,  we watch a bypass starting with two 4-fills, and box marking get a 5-star to coloring. The conclusion is a surprise. See if you can DIY this one.

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Beeby’s Elbow Quad in shye’s Catherine Wheel


This post carries us through the Sysudoku process, with the elbow fireworks of the Catherine Wheel, a second 4-set quad example from shye’s forum posts, cited in Beeby’s notes.  

From the givens grill at the end of last week’s post, there are no dublex or cross-hatch clues or subsets for the basic trace. Just a routine box marking, and an uneventful  line marking.

From the line marked grid,

here are the panels showing the elbows of the CW 4-set quad.

Matched elbows on values 1 and 2 on one corner, and another pair on values 4 and 5 on the opposite corner make up a 4-set hidden quad.

As shown last week and earlier for the shye’s other 4-set quad, the removals of 3, 6, 8 and 9 candidates are because the 4 corner cells must solve to the four elbow values.

The 1, 2, 4 and 5 removals are because, in the 4-set, only one of a pair’s two values can be placed in its neck, and placement of the other pair value in the cell opposite its neck makes that value unavailable for either one of its cuffs. An elbow’s value must be placed in one of its three cells. For each elbow pair, one value goes in the neck, and one in a cuff.  

In Beeby’s fireworks action, the 4-set quad removals leave clues (NW3, SE3, NE6, SW8), a boxline NEc8 in 1, a naked quad in NE, and NE2 alone in r2.

After this near collapse,

there is a rare opportunity for remote pairs. In a remote pair chain of even length, a candidate of each value is true in one of the end cells. So seeing the end candidates is toxic.

Now the bv field tells me to get out the crayons. The blue/green trap on 6r6c4 creates a naked pair 37 that wipes out a blue 7 and the blue army with it

I just let the green army spread into the solution.

Don’t quite get follow up traces? Just do your own spread of the green from the blue wrap and watch the trace below doing it with you.

Beeby has its own way of finishing the Catherine Wheel. Instead of the remote pairs, it does finned X wings on 6, 7, 8 and 9, then a 6-wing and that naked pair.

For a change of scenery and to make basic examples available for reference in The Sysudoku Guide, my next posts will feature several Dave Green Conceptis puzzles, 5-star and below, that illustrate basic solving resources in the three stages of Sysudoku Basic.

The first puzzle of the series has significant events in all three stages of Sysudoku Basic, the bypass, box marking and line marking. It collapses in the closing stage of line marking, just prior to advanced methods. Try it your way, then read along, following the trace move by move on your grid. You may discover something missing from your Sudoku practice.

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