floor(log3(numberOfBalls-1))+1:
up to 3^1 (2..3) balls : 1 measure
up to 3^2 (4..9) balls : 2 measures (start with up to 3x3 groups)
up to 3^3 (10..27) balls : 3 measures (start with up to 3x9 groups)
up to 3^x balls : x measures (start with up to 3x3^(x-1)) groups
floor(log3(numberOfBalls-1))+1:
up to 3^1 (2..3) balls : 1 measure
up to 3^2 (4..9) balls : 2 measures (start with up to 3x3 groups)
up to 3^3 (10..27) balls : 3 measures (start with up to 3x9 groups)
up to 3^x balls : x measures (start with up to 3x3^(x-1)) groups