two of these cells are within one region, the numbers can be assigned two ways. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. The number of classic 9×9 Sudoku solution grids is 6,670,903,752,021,072,936,960 , or around . This is roughly times the number of 9×9 Latin squares. Various other grid sizes have also been enumerated—see the main article for details. The number of essentially different solutions, when symmetries such as rotation, reflection, permutation, and relabelling are taken into account, was shown to be just 5,472,730,538 . Unlike the number of complete Sudoku grids, the number of minimal 9×9 Sudoku puzzles is not precisely known. (A minimal puzzle is one in which no clue can be deleted without losing the uniqueness of the solution.) However, statistical techniques combined with a puzzle generator show that about (with 0.065% relative error) 3.10 × 1037 minimal puzzles and 2.55 × 1025 nonessentially equivalent minimal puzzles exist. Competitions The first World Sudoku Championship was held in Lucca, Italy, from March 10 to 11, 2006. The winner was Jana Tylová of the Czech Republic. The competition included numerous variants. The second World Sudoku Championship was held in Prague, Czech Republic, from March 28 to April 1, 2007. The individual champion was Thomas Snyder of the US. The team champion was Japan. The third World Sudoku Championship was held in Goa, India, from April 14 to 16, 2008. Thomas Snyder repeated as the individual overall champion and also won the first-ever Classic Trophy (a subset of the competition counting only classic Sudoku). The Czech Republic won the team competition. The fourth World Sudoku Championship was held in Žilina, Slovakia, from April 24 to 27, 2009. After past champion Thomas Snyder of the US won the general qualification, Jan Mrozowski of Poland emerged from a 36-competitor playoff to become the new World Sudoku Champion. Host nation Slovakia emerged as the top team in a separate competition of three-membered squads. The fifth World Sudoku Championship was held in Philadelphia, Pennsylvania, from April 29 to May 2, 2010. Jan Mrozowski of Poland successfully defended his world title in the individual competition, while Germany won a separate team event. The puzzles were written by Thomas Snyder and Wei-Hwa Huang, both past U.S. Sudoku champions. The 12th World Sudoku Championship (WSC) was held in Bangalore, India, from October 15 to 22, 2017. Kota Morinishi