Spoiler for now that I had time

Case 1: No Mixed

WBB (2) - Seat 1

BWB (2) - Seat 2

BBW (2) - Seat 3

(Person in the seat can see four black stamps, so both of his must be white)

Case 2: 1 Mixed

BWM (8) - Seat 3

MBW (8) - Seat 1 (on second turn)

BMW (8) - Seat 2 (on second turn)

(If his were White or Black one of the other would of know, since no other person spoke it must be mixed.)

Case 3: 2 Mixed

MBM (8) - Seat 1 (on second turn)

(If seat 1 were black or white, player three would have know that his was mixed, therefore seat 1 has to be mixed.)

BMM (8) - Seat 2 (on second turn)

MMB (8) - Seat 2 (on second turn)

(Seat 2 can see a person with black stamps, since the other person did not know, then the other person can't see two black or one black and one white, therefore seat 2 must be mixed.)

Case 4: All Mixed

MMM (16) - Seat 2 (on second turn)

(For seat 2 the only other possiblilty would be MBM (or MWM), if that was the case then seat 1 would have known (see above), therefore seat 2 has to be mixed.)

Seat 1 - 18

Seat 2 - 42

Seat 3 - 10

So seat 2 would be the best to choice he would have 42/70 chance that the stamp you laid out in a combination that he could work out.

Case 1: No Mixed

WBB (2) - Seat 1

BWB (2) - Seat 2

BBW (2) - Seat 3

(Person in the seat can see four black stamps, so both of his must be white)

Case 2: 1 Mixed

BWM (8) - Seat 3

MBW (8) - Seat 1 (on second turn)

BMW (8) - Seat 2 (on second turn)

(If his were White or Black one of the other would of know, since no other person spoke it must be mixed.)

Case 3: 2 Mixed

MBM (8) - Seat 1 (on second turn)

(If seat 1 were black or white, player three would have know that his was mixed, therefore seat 1 has to be mixed.)

BMM (8) - Seat 2 (on second turn)

MMB (8) - Seat 2 (on second turn)

(Seat 2 can see a person with black stamps, since the other person did not know, then the other person can't see two black or one black and one white, therefore seat 2 must be mixed.)

Case 4: All Mixed

MMM (16) - Seat 2 (on second turn)

(For seat 2 the only other possiblilty would be MBM (or MWM), if that was the case then seat 1 would have known (see above), therefore seat 2 has to be mixed.)

Seat 1 - 18

Seat 2 - 42

Seat 3 - 10

So seat 2 would be the best to choice he would have 42/70 chance that the stamp you laid out in a combination that he could work out.