Brian
It doesn't appear possible with the info I have.
There are 25 Hall of Famers in the T205 set. I have 11 on my team all with different brand backs.
The other 14 Hall of Famers not currently on my team are:
Jimmy Collins
Johnny Evers
Clark Griffith
Miller Huggins
Hughie Jennings
Walter Johnson
Addie Joss
Rube Marquard
Christy Mathewson
John McGraw
Tris Speaker
Bobby Wallace
Ed Walsh
Cy Young
There are 17 different brand backs including the 6 variant tobacco brand backs. I have the 11 brands represented but not all the variants.
The variant backs not on my team are as follows:
American Beauty - black ink
Broad Leaf - green ink
Hassan - Factory 649
Piedmont - Factory 42
Sweet Caporal - Factory 25
Sweet Caporal - Factory 42 - black ink
Looking thru my T205 set revealed I have 2 more Hall of Famers I can add to my team with different backs:
Jimmy Collins - Hassan Factory 649
Cy Young - Sweet Caporal - Factory 42 - black ink
That leaves 4 more backs (17-11-2):
American Beauty - black ink
Broad Leaf - green ink
Piedmont - Factory 42
Sweet Caporal - Factory 25
I would need to add a card from the remaining pool of 12 Hall of Famers (25-11-2) with those 4 remaining backs:
Johnny Evers
Clark Griffith
Miller Huggins
Hughie Jennings
Walter Johnson
Addie Joss
Rube Marquard
Christy Mathewson
John McGraw
Tris Speaker
Bobby Wallace
Ed Walsh
Using the chart I have of possible players and back combinations shows these players and back possibilities of the 4 remaining backs for my team:
Johnny Evers - Piedmont 42
Clark Griffith - Sweet Cap - Fact. 25
Miller Huggins -
American Beauty - black
Broad Leaf - green
Hughie Jennings - Sweet Cap - Fact. 25
Walter Johnson - Sweet Cap - Fact. 25
Addie Joss - none of the 4 possible
Rube Marquard - Piedmont 42
Christy Mathewson - Piedmont 42
John McGraw - Piedmont 42
Tris Speaker - none of the 4 possible
Bobby Wallace - Piedmont 42
Ed Walsh - Piedmont 42
So it would appear I could add a Piedmont 42 and a Sweet Cap 25 Hall of Famer fairly easily but there does not appear to be a selection of American Beauty black ink or Broad Leaf green ink Hall of Famers.
Of the remaining 12 Hall of Famers in my pool, Joss and Speaker are not available in any of the 4 backs needed.
Of the remaining 10 players, 6 of them are only available in one of the missing backs...Piedmont 42
3 players are only available in Sweet Cap with Factory 25 back
So I believe it is possible to have a roster of 16 different Hall of Famers all with different backs but I don't think it is possible to fill out the roster for all 17 backs and different Hall of Fame players.
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