puzzleup 2021

jihuyao

Focus on 2/2 even case which could be 4a or 2a+2b(1a+1b on both sides).  Split one side only which is either 1a=1a or 1a<>1b.  If 1a=1a then group of 4 has 4 a and continue to compare split 4/4 of group 8 (skip for now).  If 1a<>1b then group of 4 has 2a+2b.  So all other groups only have a from which picking one and compare either side of split 1/1 and if equal then it is a otherwise it is b.  Do the same for the second 1/1 split to identify which one is b.  Done for group of 4 containing 2a+2b and split 2/2 even.  Now if split 2/2 of group 4 is uneven it implies the group of 4 has 1 b or 2 b (both b on one side).  Still focus on 2 b uneven case which implies split 1/1 of both sides must be true with 1a=1a and 1b=1b (for group of 4 having only 1 b it is 1a<>1b and 1a=1a).  Now picking any 2 from other groups which must 2 a and compare either side of 2/2 (uneven but both 1/1 splits are even).  If even that side has 2 a and if not that side has 2 b.  Done for the group of 4 in uneven case with 2 b on same side of split 2/2.  As said above group of 4 with 0 or 1 b are also identified but need further process to complete (skip for now to avoid confusion with cases of 2 b in group of 4.