Wednesday, July 29, 2020

Starting With The Seed Of An Idea - Begonia

Begonia by Yavuz Demirhan

Begonia PiecesBack in 2012, when puzzlers were puzzlers and packing puzzles were packing puzzles and not those new-fangled hoity-toity 3-piece pack jobs where you have to rotate your piece where the sun don’t shine, a seed of an idea bloomed in the corner of Yavuz Demirhan’s mind.  This seed eventually grew into our 3 dimensional reality with 3 petals.  Each 4x4 petal occupied its own plane of existence except for where the planes met.  Yavuz divided the 3 petals into 8 pieces, 4 planer and 4 non-planer, and left only the seed in place within the frame of reference.  He named his creation, Begonia.  And it was good!

Cubicdissection released Begonia in 2013 and did an excellent job in making these puzzles from Walnut and Rosewood.  The Walnut frame is solidly built and has the same thickness as the Rosewood pieces.  It also has Rosewood splines that add a nice touch.  However, the splines are very subtle and tend to blend in with the rest of the frame depending on the lighting.  All the external edges of the frame are slightly beveled to give them a nice feel.  All the pieces are beveled as well and move nicely within the frame, which is very important if you end up moving them for hours like I did.

Last Piece Doesn't FitThe objective of Begonia is to fill the 36 empty spaces within the open frame with the 8 pieces comprised of 36 cubies.  This is easier said than done.  I found myself doing the same things over and over while trying to avoid performing a completely boring brute force search.  I compromised and selected one of the planer pieces to always start with and checking all the ways that it could lie within the plane.  There are 2 main facts that I used to recognize futile attempts.  The 4 non-planer pieces have to be placed where the planes meet and the 3 empty spaces furthest from the inner corner have to be occupied by planer pieces.

I wish I could say that I used some brilliant deductive reasoning to discover the solution to this puzzle, but that’s just wishful thinking.  If the objective was to put 7 pieces in and have the remaining space match one of the already placed pieces instead of the 8th one I was holding, I think I found all of those solutions.

Begonia 3x3x4 ChallengeWhat makes Begonia so difficult is that there is a single solution and many ways to insert 7 pieces without getting the last one in.  Just for fun, I plugged it into BurrTools and found that there are 50,023 ways to put in 7 pieces without getting the last one in.  That made me feel a little better that it ONLY took me a couple of days to find the solution.

If you find yourself getting frustrated while trying to find the solution to Begonia, you could always back off and find one of the 2811 ways to build a 3x3x4 rectangular parallelepiped.  It’s much easier.  You may even be tempted to find all 2811 solutions before finding the sole solution to Begonia.

For the record, I do like those new-fangled hoity-toity 3-piece pack jobs and I’ve enjoyed solving many of them over the years.

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