I recently came across this excellent video solving a very unique Sudoku puzzle. On top of the normal Sudoku rules, there were some additional restrictions on how the digits could be placed within the grid. The puzzle solver, Simon Anthony, was initially convinced that he was being pranked and that the puzzle wasn’t actually solvable by a human.
I’m sure Simon’s initial disbelief was due to the extremely limited number of initial clues provided by the puzzle creator: two, a 1 and a 2. Explaining why requires a slight mathematical detour.
Sudoku by the Numbers
A proper Sudoku puzzle has only one solution. A “minimal” Sudoku puzzle is one in which no clue can be removed while still leaving it a proper Sudoku. Obviously, a completely blank grid is not a minimal puzzle because it could be solved with any possible unique solution.
The mathematics behind Sudoku is complex but well understood. A proof in 2012 established that the minimum number of clues for any proper Sudoku is seventeen. That is to say, it is mathematically impossible to create a minimal Sudoku puzzle (using the normal rules) that provides fewer than seventeen initial clues.
To date, only about 49,000 seventeen-clue puzzles have been discovered. And while there are nearly 5.5 billion unique and symmetrically distinct Sudoku grids, the estimated total number of minimal puzzles is on the order of 10^25. Needless to say, a seventeen-clue minimal Sudoku is a very small needle in a very large haystack.
The Miracle Puzzle
Getting back to our video, it should now be clear why Simon was sure the two-clue puzzle was not solvable — at least not in a unique way and not by normal puzzle-solving techniques.
However, this puzzle has two additional constraints (on top of the normal Sudoku rules) that severely limit which numbers can go where. By studying the puzzle in light of these constraints, Simon notices that he is, in fact, able to place a 1 on the grid, followed shortly by another. Within a few minutes, he’s placed some 2s, and slowly the grid starts to fill in.
By the end, the numbers come fast, working up through the digits one-by-one. Simon is quick to notice some beautiful symmetry within the puzzle as well, and his enthusiasm at reaching the end is delightful (“…this Mitchell Lee has come up with a work of sublime genius!”).
The Value of Constraints
What makes this video compelling — and this puzzle possible — are the additional rules around where digits can be placed in the grid. The idea of design or system constraints leading to more creative solutions is not new. In fact, our blog has several great posts on the subject. But sometimes concrete examples can be hard to find. This “miracle puzzle” is an elegant demonstration of how increasing constraints actually achieves something otherwise unachievable.
Sudoku, but the Cells Are Six Feet Apart
During the COVID-19 pandemic, we’ve all had our lives upended in uncomfortable and unpredictable ways. Lockdowns and remote work are new constraints on the way we go about our daily lives. Fully remote work was already successfully implemented by many companies, but very few employees of those organizations did their jobs in complete isolation, without ever interacting with other coworkers (or strangers in a coffee shop).
I know that my initial reaction, like that of many others, was to look for ways to make the best of a bad situation. But as the months pass and the future remains uncertain, I think it’s time to shift my attitude.
Merely waiting for things to return to “normal” is not a healthy long-term mindset. Now I’m asking myself, what can we gain from this time of new forced constraints that we can benefit from even when those constraints are gone?
Unlike the miracle Sudoku puzzle, social distancing isn’t a carefully crafted rule designed to unlock unforeseen potential. But this situation does offer us an opportunity to try things that we might otherwise consider ridiculous — home-baked bread delivered to your coworkers’ homes, collective Twitch stream invasions, grade-school-style show and tells, Friday multi-office toasts to each other, goofy welcome videos for new hires, etc. We’ve done all of these things at Atomic Object already, and I think we’re only just scratching the surface.
If you’ve tried something unexpected because of the pandemic, and it turned out surprisingly well, please share in the comments. I’d love to hear it!