Sudoku puzzles became extremely popularin Britain from late-2004. Sudoku,or SuDoku,is a Japanese
word (orphrase) meaning something like Number Place.The idea of the puzzle is extremelysimple;the
solverisfacedwitha9!9grid,dividedintonine3!3blocks:
Insomeoftheseboxes,thesetterputssomeofthedigits1¨C9 theaimofthesolveristocompletethegrid
by?llinginadigitineveryboxinsuchawaythateachrow,eachcolumn,andeach3!3boxcontains
eachofthedigits1¨C9exactlyonce
Inthisnote,wediscusstheproblemofenumeratingallpossibleSudokugrids.Thisisaverynatural
problem,but,perhapssurprisingly,itseemsunlikelythat theproblemshouldhaveasimplecombinatorial
answer.Indeed,SudokugridsaresimplyspecialcasesofLatinsquares,andtheenumerationofLatin
squaresisitselfadi?cultproblem,withnogeneralcombinatorialformulaeknown.Latinsquaresofsizes
upto11! 11havebeenenumerated,andthemethodsarebroadlybruteforcecalculations,muchlike
theapproachwesketchforSudokugridsbelow.See[1],[2]and[3]formoredetails.Itisknownthat
27
thenumberof9!9Latinsquaresis5524751496156892842531225600! 5.525!10 .Sincethisanswer
isenormous,weneedtore?neoursearchconsiderablyinordertobeabletogetananswerinasensible
amountofcomputingtime.