# Diabolical Deceptions: A 333rd Birthday Tribute to J.S. Bach

Johann Sebastian Bach is one of the most famous composers from the Baroque period. If he was still alive today, he’d be 333 years old. So, let’s celebrate 3 of his most famous works with a 33x33 loop puzzle within a 3x3 metagrid of 3+3 different genres!

## Brandenburg Concerto 3

Bach’s 3rd Brandenburg Concerto is a 3-movement piece, mainly featuring its 3 violins, 3 violas and 3 cellos. In this spirit we have 3 base genres each with its own qualities:

1. Masyu: On a white pearl the loop goes straight but turns on at least one side. On a black pearl the loop turns but goes straight on both sides.
2. Balance Loop: On a white pearl the loop goes straight and extends out the same distance either side. On a black pearl the loop goes straight but extends out different distances from either side.
3. Inside-Outside/Every Third Breakpoint: On a white pearl the loop turns so that more of the cell is outside of the loop than inside. On a black pearl the loop turns so that more of the cell is inside of the loop than outside. Additionally, regardless of all other rules, if the loop is cut into ‘segments’ at each pearl it passes through, any segment which has any part in a region where this is applicable (even if it is only half a cell-width long) either: a) is exactly one cell-width long; or b) turns exactly twice.

## Well-Tempered Claviers

Bach’s most significant works for a keyboard instrument are his Well-Tempered Claviers, which advocated the use of well-temperament through a prelude and fugue in all 24 keys, one for each of the two volumes. Many of the preludes are quite simple (e.g. the prelude in C major from book 1) so here is a simple global rule:

• Yajilin: Draw a loop connecting cell centres of some pairs of adjacent cells. Shade any cell the loop does not pass through black. Then no two black cells may be orthogonally adjacent.

However, the fugues are more complex, and the majority (26) contain 3 individual voices. In recognition of this, we have 3 deceptions:

1. Deformation: Any white pearl may be shaded black and function as a black pearl (this does not count as a shaded cell for the purposes of the Yajilin global rule). All pearls in these regions must be passed through.
2. Optional: Any pearl may not be passed through, however as in the Yajilin global rule the cell containing the pearl must be shaded black and not be adjacent to any other cell which is also shaded black.
3. Grey: To make 3 colours, a grey pearl is a pearl which does not satisfy the requirements for being either black or white for its genre. Exactly one pearl in each row and column must be turned grey. All pearls in these regions (including grey pearls) must be passed through. Note that this rule does not change the Every Third Breakpoint base genre requirement – grey pearls act the same as white and black pearls in this regard.

## St Matthew Passion

Our 3rd and final work today is the St Matthew Passion, an extravagant work for double choir and double orchestra illustrating a combination of different melodies and harmonies working as one. So, in honour of this combination of voices and instruments, we have a grand finale:

• Graeco-Latin Square: In the 3x3 metagrid, each of the 3 base genres and each of the 3 deceptions appears exactly once in each row and column, with exactly one base genre and deception per square. Furthermore, each base genre-deception pair occurs exactly once. The Yajilin global rule always applies.

Good luck, and enjoy!

Sorry for any factual inaccuracies. Thanks to @edderiofer and a non-user for testsolving! Inspired by The Ludicrous Loop: over a thousand cells of circular logic! - if you haven't tried this you should try it too!

None of the deceptions allow four blacks in a row for Masyu nor do they allow bbbwww. Therefore, the middle right grid must be Masyu. $$\begin{array}{|c|c|c|}\hline-&-&-\\\hline-&-&Masyu\\\hline-&-&-\\\hline\end{array}$$
Inside-Outside cannot have black pearls on the border. Therefore, the top right grid must be Balance Loop. Furthermore, normal Balance Loop cannot have a pearl in a corner so the deception for that grid must be Grey $$\begin{array}{|c|c|c|}\hline-&-&Balance/Grey\\\hline-&-&Masyu\\\hline-&-&-\\\hline\end{array}$$ The white crosses in the Masyu grid won't work with the Optional deception: if the middle pearl were not optional, it could not turn on either side. If it were optional then the four neighbouring white pearls would make a square loop around it. Therefore, the deception for that grid must be Deformation and the bottom right grid must be Inside-Outside/Optional $$\begin{array}{|c|c|c|}\hline-&-&Balance / Grey\\\hline-&-&Masyu / Deformation\\\hline-&-&In-Out / Optional\\\hline\end{array}$$ The bottom left grid must now be either Masyu/Grey or Balance Loop/Deformation. However, again because of the corner pearl, Balance Loop is not possible so it must be Masyu/Grey $$\begin{array}{|c|c|c|}\hline-&-&Balance / Grey\\\hline-&-&Masyu / Deformation\\\hline Masyu / Grey&-&In-Out / Optional\\\hline\end{array}$$ After that the Graeco-Latin Square fills itself $$\begin{array}{|c|c|c|}\hline In-Out / Deformation&Masyu / Optional&Balance / Grey\\\hline Balance/ Optional&In-Out / Grey&Masyu / Deformation\\\hline Masyu / Grey&Balance / Deformation&In-Out / Optional\\\hline\end{array}$$