Strain field in deformable solid (continuum) has to follow compatibility equations so as to ensure single valued continuous displacement field. There are in all 81 such equations and most of them are repeated, finally we are left with 6 equations. It is quoted in text books that only 3 out of these 6 equations are independant. If it is so why we need to use six equations to ensure possibility of strain field? Only three equations should be enough. Please help.