This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372224 #35 May 25 2024 09:04:41 %S A372224 0,1,2,4,6,8,12,14,17 %N A372224 The size of the smallest critical set of hints needed to uniquely solve a generalized n X n Sudoku board. %C A372224 A "critical set" is a collection of Sudoku hints that uniquely determines a solution to the puzzle, but such that removing any hint no longer does so. %C A372224 Our generalized n X n Sudoku board consists of n rows, n columns, and n lengthwise rectangular subgrids with dimensions A033676(n) X A033677(n). Every row, every column, and every subgrid must contain the digits 1..n. %C A372224 When n is prime, a(n) is the size of smallest critical set of an n X n Latin square, which is conjectured to equal A002620(n). %D A372224 J. N. Cooper and A. Kirkpatrick, Critical Sets for Sudoku and General Graphs, Discrete Mathematics, 315-316 (2014), 112-119. %D A372224 C. Lass, Minimal number of clues for Sudokus, Central European Journal of Computer Science, 2 (2012). %D A372224 G. McGuire et al., There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration, Experimental Mathematics, 23 (2012), 190-217. %H A372224 H. Chel, D. Mylavarapu, and D. Sharma, <a href="http://doi.org/10.1109/ICEEOT.2016.7754798">A novel multistage genetic algorithm approach for solving Sudoku puzzle</a>, IEEE International Conference on Electrical, Electronics, and Optimization Techniques (2016), 1. %F A372224 When n is prime, a(n) is conjectured to equal A002620(n). %F A372224 When n is square, a(n) = A198297(n). %e A372224 Below is a critical set of size 17 on the 9 X 9 Sudoku grid: %e A372224 . %e A372224 +-------+-------+-------+ %e A372224 | | 8 1 | | %e A372224 | | | 4 3 | %e A372224 | 5 | | | %e A372224 +-------+-------+-------+ %e A372224 | | 7 | 8 | %e A372224 | | | 1 | %e A372224 | 2 | 3 | | %e A372224 +-------+-------+-------+ %e A372224 | 6 | | 7 5 | %e A372224 | 3 | 4 | | %e A372224 | | 2 | 6 | %e A372224 +-------+-------+-------+ %e A372224 . %e A372224 which uniquely determines the solution: %e A372224 . %e A372224 +-------+-------+-------+ %e A372224 | 2 3 7 | 8 4 1 | 5 6 9 | %e A372224 | 1 8 6 | 7 9 5 | 2 4 3 | %e A372224 | 5 9 4 | 3 2 6 | 7 1 8 | %e A372224 +-------+-------+-------+ %e A372224 | 3 1 5 | 6 7 4 | 8 9 2 | %e A372224 | 4 6 9 | 5 8 2 | 1 3 7 | %e A372224 | 7 2 8 | 1 3 9 | 4 5 6 | %e A372224 +-------+-------+-------+ %e A372224 | 6 4 2 | 9 1 8 | 3 7 5 | %e A372224 | 8 5 3 | 4 6 7 | 9 2 1 | %e A372224 | 9 7 1 | 2 5 3 | 6 8 4 | %e A372224 +-------+-------+-------+ %Y A372224 Cf. A002620, A002860, A198297. %K A372224 nonn,hard,more %O A372224 1,3 %A A372224 _Agustin Gomez de la Vega_ and _Mithra Karamchedu_, Apr 22 2024