Tag Archives: optimization

Special Puzzle 11: Canon and Gigue in D

Musical Marathon This is an optimization puzzle. Lay groups of notes on the grid and program a robot to move along a path. When the robot moves on top of a group of notes, the exact group of notes is played. When the robot moves on top of a cell without any group, the previous note is simply held. A group of notes is played for a quaver (half of a quarter, eighth of a measure), so the robot moves at the speed of two units per beat. The given score must be played precisely. The robot may not stop; they must move to an orthogonally adjacent square every quaver. Optimize by using the least number of notes.

Here is the puzzle (Canon and Gigue in D by Johann Pachelbel), and an example solution by me that is fairly optimized (31 notes):

Special Puzzle 11: Musical Marathon

Special Puzzle 11: Canon and Gigue in D
Musical Marathon
(MIDI if you want to listen instead of read)

The path is the following, starting from the black-bordered square (B indicates introducing the robot):
B↓←↑→↓←↑ / →↑↑←↑↑→→ / ←↓←↑→↓→→ / ↓→←↑↓↓←← / →↑←↓→↓↓→ / ←→→←←↓→→ / →↓↓→←←↑← / ↑→↓←←←←↓

(You can imagine it. Sadly I don’t have an applet to play it or something. I need to make some applets heh 😛 )

Yes, as you can see, I’m into optimization puzzles too. Also, I listen to too many songs and I recently (re)played SpaceChem, so…yeah.

I also have a 33-measure (264-quaver) song soon. I only need to create the score 😛

Bridge Puzzles

Revisiting an old Bridge puzzle posted in this blog about 9-11 months ago, now generalized to 8 variants.

Optimize: Get the total HCP held by a partnership as low as possible, such that there exists a pair of hands with a total of that much HCP and a) for any, b) for some configuration of hands that the other partnership is holding, and given a) best play, b) worst play from the opponents, you can always get a contract of a) 7S, b) 7NT.

My solution for aab (for any, best play, 7NT) was 19 HCP. I’ll try to get all solved.