Metcalf’s Second Patterns Game Entry

This post reports a Sysudoku solution path for Mike’s second Patterns Game entry on a extraordinary pattern of givens. As a successful entry, I believe it had to meet the contest requirement for a simpler solution than is found here. Maybe a reader can show us one.

In that bypass challenge offered last post, how far did your bypass go in the box marking below without writing down any of the unpaired box slinks? It doesn’t really matter, but it’s fun.

Here is the box marked grid, for comparison to yours.  Uncertainty persists in three corner boxes.

Now when line marking fills out the candidate grid, you’ll see how you might slug it out with the patterns game referee.


On the line marked grid, with necessary fill strings, the first advanced moves are two hidden unique rectangles of Type 1.

Hidden UR’s are not what anyone has in mind for “singles”. There must be something else here that does not depend on them.








The  8r1c9 hidden UR removal enables a Sysudoku favorite, a BARN, a Bent Almost Restricted n-set. One value group, the only bent one, is toxic. Not a “singles” move.

The next move comes from the more advanced and laborious search described in the Sysudoku Guide as AIC Building. In AIC Building, you try to keep going any AIC slinking from any cell by any AIC means, until it reaches another candidate seeing its value in the starting cell. Expect it to take time and patience, although each AIC fun to build. Just have multiple copies of the grid to scratch up, or like me, just make many ©PowerPoint screen copies of the grid.

There’s at least one decisive boomerang here. Starting with a 9-chain from the bv cell r3c6, a reversed bv in r5c6 continues the AIC as a grouped 8-chain to the XY node switch to the 1 seeing its match in the starting cell. The boomerang’s return creates an Almost Nice Loop. If the starting cell is a bv, it’s a confirming ANL, otherwise, an eliminating ANL.

There are a lot of starting cells and possible closings. I’m not venturing to say how many boomerangs are on this already simplified grid.

But AIC Building isn’t singles. The grouped AIC boomer is decisive, triggering a “singles” collapse.

We move on next week to Brian Challenger’s Super Fiendish 7. Did you get your copy yet?

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Tracking a Patterns Game Entry

This post and the next explore two entries in the online Sudoku composing contest known as the “Patterns Game”. The contest is between Sudoku composers:  who can submit first puzzles with unique solutions that fit a “pattern” of givens issued by the referee. The pattern fixes the cell locations,  but not the values, of the givens. Computer apps available to the contestants arbitrate the contest rules on difficulty limits and guard against morphs of previous submittals.

One winning Patterns Game entry by Mike Metcalf was previewed last post as ‘mike 1’. The second, ‘mike 2’,  will be previewed here and solved next post.

The boundary between the clutter avoiding bypass and line marking is often determined by how many marks you are willing to keep in your head. In this case, let’s say you drew the line at this bypass:

Is that too challenging? It’s a little much for me, but reasonable for many Sysudoku readers.  I’m dropping back to full line marking to be sure every reader can appreciate what talented players see in the bypass above. Here’s the box marking grid just before C7 in the box marking trace below.

The 7: list effects trace had to be folded to fit on the screen.

Box marking and line marking don’t require exceptional talent, just patience and enough interest in Sudoku.

The bypass, box marking and line marking cover what is generally known as “singles”, but go further to return cell position marking of all strong links defined by boxes and lines.

Here is the grid on the line marking encounter of a naked triple on the 6th marked line. The removal of 9r2c1 can be interpreted as a box/line removal triggered by the r1 9 removals.  Or you may just note that the 9 removals leave 9r2c1 within sight of all remaining 9’s in r1.

In the Patterns Game, all puzzle rules require entry puzzles to be solved by “singles”.  Though often used, that term is not well defined. But in the game all participants use the same solver, so “singles” in this rule means what the solver says it is. Since mike1 is a winning entry, we expect unit subset removals must be “singles”.

Line marking is completed with lines  r1 and r2, leaving columns c8 and c9 for closing.

The line marked grid hosts two hidden unique rectangles of type 2b.  They must be superfluous though, because, looking at the UR table on the Tools page, hidden UR  can’t be considered “singles”.

Next, my cluster stalls. Gordon and I independently  find an XY ANL with terminals 8r2c1 and 8r2c5. The terminal 8’s on the same line wink to convert the ANL into a nice loop, with extra removals.


Gordon finishes with an enabled XY-wing and a “singles” collapse.


I have to go with my investment in coloring. The cluster expansion, accelerated by nice loop coloring, wraps blue in c8, for a very green solution.






Next week, it’s Metcalf’s Pattern Games second entry, mike 2.


Do you have a third one? To find a pattern game entry, you test set after set of placements on the pattern.  If your solver is in human action mode, it stalls over and over. If its in tree traversal mode, you get hundreds of stalls and multiple solutions over and over. Hats off to the patience of patterns gamers.





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FTSPAH 124 and 184 Close the Review

The FTSPAH review ends with a puzzle that might indeed frustrate experienced solvers, number 184.  It appears to require AIC building.  After the details, this post ends with a bypass trace of 124 which begins with three line 3-fills, and collapses in response to the first of them.

Hints of toughness are all along the basic trace of FSTPAH 184. There is no given 8, and puzzle resists the bypass, and denies a productive 3-fill.  There is no bail out in box marking, and 184 hangs tough in line marking  until a 6-fill clears some clutter before the last line, a 7-fill.

Here’s the grid at the naked pair r7s39. It has to be frustrating to search for advanced structures in the  keypad  version of this grid.

In this one, bi-value cells and strong links are marked and visible.  Anyone interested in tough Sudoku can learn this much ©PowerPoint.

The first advanced move is often an XY chain Almost Nice Loop, an XY ANL, as it is here.  The systematic XY railway method makes the spotting easy. Curves are drawn connecting like values to form the railway, which is explored for repeated values defining XY ANL and nice loops.

But now 184 somewhat justifies the cover warnings by demanding AIC building. In this phase, AIC chains are extended by all means necessary from slinks emerging from cells in the attempt to close a loop on the starting cell. With so many possibilities requiring detailed exploration, AIC building can be frustrating, and cursing doesn’t seem to help a lot.

A long 4-chain with several terminal pairs but no ANL victim is extended by a 6-chain into a bv boomerang confirming 4r8c4.

It looks deceptively easy, once you find it. The problem is following the humanly practical process that has you looking there.



Next, an AIC starting at 4r1c3 to 4r5c3 continues to find another slink until it returns, not to 3 or 6 for a boomerang elimination, but to 4 for an AIC nice loop. Now every outside candidate seeing both ends of any link is eliminated. Four more bv are created.




The bv added in AIC building make coloring much more attractive. In the first cluster, two candidates are trapped. They see the same value in one color, and share their cell with the other. Blue or green, these two are eliminated.




Next, either an r5 slink or the naked triple Cnt256 traps 5r4c5, and the resulting r5s38 removes 8r7c5.








In the expanded bv map, an XY ANL removes 3r9c1.










Then a second XY ANL removes 8r8c9, for c9s13 and SE5.










the blue departure brings immediate collapse.










As promised, the last word on  the FTSPAH  review is the bypass collapse of 124. The only possible frustration here is a discovery that you missed an effect in the rush of them.


The next collection up for Sysudoku review is Sudoku Super Fiendish, by Brian Challenger. It is a small collection of 100 puzzles. The 10 – puzzle sample,:  7, 17, 27, …, 97, covers 10% of the collection. For that reason,  the review will preview the givens for only the first review puzzle, SSF 7. To work ahead further, you’ll need to order your own copy.

You’ll have some extra time because the next two posts will deal with two entries in an interesting Sudoku puzzle contest, known on the Enjoy Sudoku forum as “the pattern game”. My friend Gordon Fick sent along two successful entries by Mike Metcalf based on the same pattern.

Here we will call them ‘mike 1’ (shown here) and ‘mike 2’ to follow next post.  If you are not already, you might pretend to be a pattern game contestant, and make up your own mike 2. Even with a solver to check each effort, it’s not easy.

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Two more Basic FTSPAH, 64 and 164

FTSPAH 64 exits in the bypass, and illustrates several bypass tactics that avoid the curse – invoking frustration that the  composers of FTSPAH puzzles claim on their cover. Its post partner 164 illustrates more bypass moves and survives for a few line markings.

Several 64 tactics show up as the bypass begins. Starting the box scan in NW, NW1 is not revealed until we survey the claims on the W box, forcing a 1-slink in Wc3, and a dublex crosshatch into NW, for W1. Our immediate response to the little square is to scan side lines r1 and c3 for values forced into the side lines of the square. Immediate response to little squares, filled box corners, walls, and 3-fills is the second tactic.


Moving on to value 2, two cross hatches fail, then a dublex crosshatch gets W3, and triggers the third tactic, which is to look back for slinks of previous values now converted to clues. That unwritten 1-slink leading to NW1 now produces W1. When value 4, clues E4 and E5 force these values into r4c14. N4 determines W4 and C5.

While text descriptions like the above explain the nature of Sysudoku marking, and specific solving events, it is much more effective to duplicate the traces while filling out the grid from the givens, as you anticipate and confirm each step, and let no action escape justification.



A Sysudoku trace trails off when complete placement is obviously no longer dependent on critical effects.

Turning to FTSPAH 164, an E box 3-fill gives a good beginning, followed by the first of several instances of two values working together to claim two cells in a box or line. In this case it’s 4 and 5 claiming cells of the W box and r5 line.  This leads to the grid shown here in which you are  to account for NE6. To add some handy names, it’s the NW four corners  and  N wall.

In the remaining bypass, some effects have multiple causes. Sysudoku conventions determined which cause gets there first, but unless you’re writing traces you expect others to compare with theirs, the conventions  don’t matter.




Here is the line marking grid at the naked single SE9 triggering the collapse.








Next time the FTSPAH review concludes with a third bypass wipe out 124, and with 184, the only puzzle to require AIC building. The FTSPAH review table below records five of ten basic finishes, three of these in the bypass. The advanced puzzles are dominated by XY chains and coloring. With the exception of 184, there’s nothing to justify the bravado of the title, and the breathless hype of the cover descriptions.






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FTSPAH 104 and 144

The review of the unspeakable FTSPAH continues with two more puzzles selected arithmetically.

The basic trace of FTSPAH 104 is Sysudoku Basic at its best. A near collapse in the bypass is extended by a deferred hidden dublex, which 104 survives, only to collapse in early line marking.

The hidden dublex leads the third run in a very productive bypass.












Imagine being at the SEhdx3  grid as a trace reader, with the task of accounting for SE3. Is your conception of the hidden dublex  sufficient for spotting this one. It may need tweaking.





Now just before the point where SEhdx3 is pulled out as a cause of the SW3 list, the trace identifies a hidden single. It must be spotted in reaction to SE2. Would you have spotted it without the trace?

When you do, you’re closer to the end than you might think.



FTSPAH 144 offers an early spotting challenge, namely N3 in this grid.









Later in line marking, something harder, a hidden pair r5hp59. A hidden subset is n values confined to n cells, and therefore claiming them. More abstractly, it’s n values that can be placed in only one way.

Much easier to spot, and the equivalent, is the corresponding naked triple r5nt246.

Here is the basic trace leading to these spotting chances.  The systematic and repeatable process of Sysudoku Basic, with a focused response  to each grid change, replaces unfocused search in a sea of candidates.


The horde of bv on the line marked grid invite two equally systematic advanced methods, XY chains and coloring.

The XY railway delivers less than expected, but the XY ANL elimination 4r1c8 is decisive in coloring.



In the blue/green cluster the trap at r3c8 leaves a hidden single 4 in c8.












expands the cluster to wrap green in c7. The blue collapse is immediate






Next is FTSPAH 64                                                                                   and 164.

Both are finished in Basic, and one in the bypass.





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Systematic FTSPAH 44 and 84

This post demonstrates two more FTSPAH unlikely to frustrate anyone following the Sysudoku order of battle.

FTSPAH 44 begins with an unusually large number of givens, which generates a correspondingly large number of 3-fills. In fact, the givens offer both the box 3-fill NE[457] and the line 3-fill c7[357].

In Sysudoku traces, we mark 3-fills by naming the unit, then listing the three missing values. Line 3-fills are harder to spot, but are more often effective.  In the blog, these differences have led to the following marking conventions:

Line 3-fills are marked in the trace, and in the fill list space on the grid when the fill isn’t immediate.

Box 3-fills are marked only in the trace, ahead of line fills, and only when a fill occurs immediately.

Both types of 3-fill are marked ahead of the 1 to 9 values list.

FTSPAH 44 can be solved in the bypass by starting with the 3-fill c7[357], but the box 3-fill NE[457] is even faster. The first run includes three filled 3-fills.

In the grid at the end of the first run, the centered pencil marks are clue effects, in reserve for retrace causes.

In the grid at the end of the first run, the centered pencil marks are clue effects, in reserve for retrace causes.

The bypass trace follows below. There is no pause in which to utilize the c6 line 3-fill.

FTSPAH 84 starts with the value list, and nothing to say until value 5, then a series of head scratching, but rewarding effects.  Two unlikely hidden dublexi keep it going.  At the end of the first leg, a naked pair C36 combines with an earlier W6 for a one hdx. Then, on the second leg headed by NW8, an amazing hidden dublex. C4 on the first leg combining with NW4 on the second, deserves a spotting gold star.

Box and line marking are easy, and FTSPAH 84 goes on to deliver some advanced satisfaction.

First, on the line marked grid, a double hidden unique rectangle, Type 2b. Each 9-slink connecting floor to ceiling forces  a reversible solution rectangle when the other UR value is placed in opposite ceiling corner. For the r8 slink, that’s 3r9c8. For the r9 slink, its 3r8c8.

The Guide explains  how slinks work in the hidden UR.


In the same area, the 3r9c8 removal creates an XY-wing that pushes 84 over the edge.



The predominant 1,2,3 values hold their relationships close until the ball starts to unravel.


Next week continues the FTSPAH review with 104 and 144.



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The FTSPAH Review Begins With a Tour

Here I report on 4 and 24, the first two of 10 puzzles selected for the Sysudoku review of the FTSPAH puzzle book. Starting grids were displayed at the end of last week’s post.   I also explain a few things about the blog to a high school classmate, Jimmy.

FTSPAH has no acknowledged author, publisher, or copyright notice.  The full title is spelled out in the previous post, and that’s quite enough.  We are told it comes from Middletown Delaware, and that its “200 DIFFICULT puzzles … have the ability to cause even the most seasoned Sudoku lover to curse out loud in frustration”. Sysudoku readers are not expected to be all that seasoned. A Sysudoku review shows what can be expected by a human solver following the Sysudoku plan of attack. FTSPAH is revealed to be not that frustrating.

Here is the bypass trace for FTSPAH  4. The given 2-fill and 3-fill have so many effects, the puzzle is essentially solved before the 1-9 values list begins.


Jimmy, traces allow readers to reconstruct the solution one move at a time. The reader provides the reason for each move. That makes it simple and informative.  Experienced readers can write their own traces and compare notes.  For help, see Sysudoku Traces on the menu bar.

Sysudoku Basic on Ftspah 24 is more normal. The challenge here is patient focus on your knitting.




The first advanced stop is the BV map, where the XY railway produces a simple XY ANL.

Jimmy, there’s a glossary on the menu bar. It’s Sysudoku Speak.





Basic is the collection of candidates. Advanced is using relationships of candidates and clues to remove false candidates and confirm true ones. All basic procedures and advanced methods are explained in a hierarchy of pages, The Guide. For a listing of post titles, go to Titles.

Then an XY extension of the XY chain winds through the bv field to produce a very long nice loop. Every pair along the loop is toxic. Every link of the chain includes a true candidate, a placement in the solution.

By Sudoku rules, two placements of the same value cannot be in the same box or line. So any candidate in a box or line with both link candidates of the same value is removed.

The strong link network reveals itself in X-chains and coloring. Here we get a 2-chain ANL. In an ANL, an Almost Nice Loop, at least one terminal is true. If you see both, you’re out.






Coloring reveals a lot more of the slink network. Traps at r3c3 and r7c3 expand the cluster to force a wrap of green in r1c5. The blue army mops up.

One color is true, therefore seeing both colors of the same value is fatal. Two candidates of the same color in a cell is fatal for that color. That’s one type of wrap.


Here, the trap of 9r7c3 colors 9r7c1, and that traps 3r7c1, because blue or green is true.

Jimmy, I don’t usually repeat the fundamentals, but in this post it’s to show you around the place.

Next week we pair FTSPAH 44 at left with 84  on the right. One is basic level, the other, advanced. Find out which before the post comes out.


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