The idea for Just One Cell Sudoku was formalized in 2010 by Thomas Snyder and Wei-Hwa Huang for the 2010 World Sudoku Championship in Philadelphia as a way to test sudoku-solving skills without allowing guessing. There had been an unfortunate trend in some prior championships of having very hard puzzles with “unique” solutions but no logical steps to reach them, or those steps not being worth the time to find versus other short cuts. A Just One Cell Sudoku sets up skill-specific challenges that can test any kind of step like Pointing Pairs or X-wings and Y-Wings and beyond, without allowing guessing/bifurcation to be useful in any way. One of the ten individual rounds at the event contained only these puzzles, and the overall champion of the event (Jan Mrozowski) was also the top scorer in the Just One Cell-focused round by 15%.
A Just One Cell Sudoku is not a full puzzle, and some might not even label it as a proper puzzle. Instead it is a concentrated, bite-sized piece of Sudoku thinking. One can draw an analogy to other competitions like Chess problems for the game of Chess. A Chess problem (e.g., “white to mate in 2 moves”) requires some of the visualization of moves as in the full game, and can highlight unusual sequences unlikely to come up with a game. But it is not the same as playing a full game of Chess and may be enjoyed in different ways.
Just One Cell Sudoku can have a minimal number of given numbers to clearly highlight an idea, more as a tutorial or teaching opportunity. For example, providing just 8 carefully positioned numbers can show how to find a “naked single” in just one cell, where the 9th remaining digit is the only choice. (The “just enough” concept is used frequently in visual instructions alongside puzzles but not as often in puzzle compositions, and we note this idea can extend to lots of puzzle styles not just Sudoku.)
Just One Cell Sudoku for regular play may also have extra numbers (“noise” on top of the “signal” from the minimal givens) so that searching for the prime spot to make progress is harder. Because each grid is effectively a single sticking point with only one next place to make progress, for awhile most solvers will find Just One Cell Sudoku to be medium-level or harder until they have more experience drilling techniques of scanning and finding patterns that may clue potential break-ins. Some puzzles may be easier than expected, like a solver very strong at hidden information like hidden singles and pairs if the puzzle uses those; but everyone has blind spots and Just One Cell Sudoku will reveal them.
Just One Cell puzzles are useful for training but also for practicing puzzle construction. Thomas Snyder / Dr. Sudoku now extends the idea when making classic sudoku to try to have the first few digits follow a specific path just like a Just One Cell Sudoku. See these two examples from the Twelve Days of Sudoku of extending a Just One Cell idea to a full puzzle with the grids being indistinguishable for awhile.

Above is the first (hard) example Wei-Hwa and Thomas gave for the 2010 WSC. After the break you can see a set of images showing the path to the one cell / one number answer.
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