32. First Peak: Sudokus are all about constraints … except when they’re not

With the exception of one important detail, First Peak is a Sudoku that exhibits the same pattern found in Platinum Blonde, Golden Nugget, and coly013 and in transposed form in several other puzzles for which there are videos on this channel. (See the comments on video #31.) In First Peak, the design is turned 90° to the right, but the “script” for the solution follows the same lines as in the other cases.
Specifically, the instances of three numbers are recognized to occur among the “givens” in such a way that if two of them are placed in certain cells, and one of those two numbers is then placed in two corresponding cells in a block in the same row or column, this locates several other instances of those numbers. Typically the other of those two numbers also ends up in corresponding cells in the third and remaining block in that row or column. The third of the original conspicuous numbers is then added to one of the other two that is “solo” in a pair of cells. This places many instances of that third number as well as remaining instances of the first two. The need to avoid repeating the original pair in a rectangle, and then to avoid an AB-BC-AC arrangement of the three numbers, moves things along at key points. The puzzle grows in complexity, even as more cells are filled in, until it reaches a “culminating point.” A tactical approach must then be found to break through an impasse. Once that is done, everything fills in smoothly to complete the solution. That is the classic script, and First Peak follows it very closely.
So in what detail does it differ from the other eight Sudokus on this channel that also follow the same script? In the case of those other puzzles, two of the three conspicuous numbers must go in the cells where they were supplied to start the solution going. Those are the only options for those cells: AB, BC, or AC. In other words, those possibilities are constrained. In this case, there is a further option. Besides the 2, 3, and 5, a 4 can go in one of the cells. That means that it is not at all certain that any of the three possibilities 23, 25, or 35 will work. They are not constrained.
Many Sudoku solvers would therefore not try them, and I certainly respect that position. There is indeed great satisfaction in identifying what is logically compelled and using that information to reach a solution, and I wish every success to those who are pushing the limits of that approach by discovering how it can be applied to more and more difficult puzzles.
However, I did try those numbers. Their positions among the “givens” seemed suspiciously advantageous, and I found that when I worked with them, they were so “lively” that they had to be up to something. And this indeed solved the puzzle. So even though Sudokus have been well defined as “constraint satisfaction problems,” sometimes they seem to take on a life of their own that transcends their constraints.