# Tag Archives: Unsolvable 40

## Cell Forcing Chains

Here we examine forcing chains starting from all candidates in a cell.  When the number of chains is 2, there is nothing new.  Above that,  there is a new strategy to explore, which rivals LPO in complexity, but falls behind … Continue reading

## Unsolvable 40 Logically Solved

In this post we checkpoint the solution of Stuart’s Unsolvable 40, via LPO and a coloring cluster extended by pattern slinks.  The solution of this puzzle by pattern analysis expresses well the ideals of Systematic Sudoku, and demonstrates what can … Continue reading

Here I introduce a new form of strong link, the pattern slink.  The letter assignment panel for pattern enumeration in LPO identifies such slinks.  Every unit induced slink between a number’s patterns identifies two mutually exclusive sets of patterns.  This … Continue reading

## Scrounging for New Pattern Sets in LPO

Here we attempt a more satisfying victory over the Stuart Unsolvable #40, by using the pattern reductions of the first pattern sets to add new pattern sets, moving closer to the full Pattern Overlay Method.  This series of posts on … Continue reading

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## Searching for Orphans in LPO

This post illustrates the search for orphans in my Limited Pattern Overlay method.  Orphans are what we going to call candidates not belonging to any completed pattern.  Orphans are found by means of the freeform diagrams, as illustrated in Pattern … Continue reading

## Unsolvable 40 is Solved?

In the last post, Unsolvable 40 was staggered by a remarkable combination of coloring and LPO.  Only one pattern, 8b, was removed by LPO conflicts.  But other conflicts combined to force another pattern 8c to the color blue in an … Continue reading

Posted in Extreme Solving | | 1 Comment

## LPO vs Unsolvable 40

This post applies Limited Pattern Overlay, the sysudokie’s POM, to an Andrew Stuart Unsolvable, #40. The interplay of coloring and LPO patterns ties this beast up for the kill. Here is the grid as we apply LPO: My freeform LPO … Continue reading