Solve Along: Bubbly (MIT Mystery Hunt 2019)

In this video I solve the puzzle Bubbly from the 2019 MIT Mystery Hunt

Along the way I cover the general strategy of solving impartial games and applying the Sprague-Grundy Theorem of combinatorial game theory, using Bubbly as a practical example.

0:00:00 Introduction
0:02:24 Reading the puzzle and solution writeup
0:06:11 The board game: good and bad states
0:12:49 The board game and Bubbly
0:15:36 Bubbly example: the opts function
0:22:59 Bubbly example: the graph
0:27:58 Bubbly example: good/bad states
0:33:34 Solving the Bubbly example in Python
0:38:19 Caching for larger examples
0:41:04 Complete Bubbly opts function
0:50:34 Bubbly opts function in Python
0:56:54 Solving Game #1 in Python
1:02:07 Naming the moves: the popts function
1:09:39 Solving Game #2 in Python
1:12:39 The parsestate function
1:14:48 Solving all games in Python
1:17:51 Python solution recap
1:20:32 Puzzle extraction
1:22:44 Board game nimbers
1:29:19 Bubbly example: nimber analysis
1:35:28 Nimber addition
1:43:38 Bubbly nimbers: simple examples
1:50:00 The Sprague-Grundy Theorem
1:54:02 The missing nimber formula
1:55:32 Puzzle solution writeup Python program
1:59:10 Revisiting our Python solution
2:03:22 Single-bubble state nimber formula
2:08:55 Bubbly nimber formulas summary
2:11:12 Composite state nopts formula
2:16:40 Bubbly nimbers: complex example
2:21:00 Game #1 solution by hand
2:31:53 Game #2 solution by hand
2:37:20 Game #3 solution by hand
2:43:46 Game #4 solution by hand
2:48:18 Game #5 solution by hand
2:52:16 Game #6 solution by hand
2:56:23 Game #7 solution by hand
2:58:45 Conclusion

[chenzhang]

This is excellent content. As an avid puzzle hunt lover but one not nearly good enough yet to solve Mystery Hunt puzzles. It's so great to see the thinking that goes into solving one of these. Thank you for making these and I hope you keep them up.

[IsaacBD]

So glad I found this channel! Puzzle hunt solve-alongs are my new favourite content.

[kilimanjarocruz]

Fantastic all the way through. Very enlightening .

[arcynical]

Not gonna lie, I've never ever heard someone pronounce champagne like that. That said, I'll watch the rest. This will be great and completely over my head!

[martonnemeth]

I'm not nearly good (or patient) enough to solve any puzzle, that you've featured so far. As I work with a lot of these games, and would've instantly thought of making a program to work it out, I think I might've had a shot at this one.

[mikemannis]

Excellent video. It obviously took a lot of effort (and even more than I initially realized, based on your final comments about it), so thank you! I will certainly share it with others who are potentially interested in this type of material. Out of curiosity (if you see this comment), which team do you hunt with?