420 HITCHCOCK. 



the second group is needed as A' increases. When A 7 = 5 both groups 

 are complete only in the case A" = 2. When A 7 = 6 we shall need part 

 of a third group only when A = 2 or 3. These and many other facts 

 can be seen at once by a table of the numbers used in the discussion : 



Case N = 3: 



