The puzzle presented below is derived as a variation of the Blue-eye paradox" which has been discussed in the following thread. https://www.physicsforums.com/threads/blue-eye-paradox.875870 THE PUZZLE Teams of N people each are each given the following challenge. The rules for the challenge contest are shown indented below, and they are presented to each team member before the contest begins. Each person, in a private room, is blindfolded and is assisted in putting on a pullover shirt which has a four inch diameter dot on the back between the shoulder blades. Randomly, for each team, W of the members wil have white dots and B of the members have black dots. N = W + B. Also, W > 1 and B > 1. The value of W is chosen randomly for each contest, and it is the same for each team, but the value is not revealed to the teams. The blindfolds are removed, and all of the team members go into a large common room. Each team member can see the colors of the dots on the back of all the others, but not her/his own dot. There is no way a peson can see his/her own dot. No one is permitted to communicate in any way about the color of any other person's dot to anyone. Any such communication will disqualify the team. After a few minutes, sufficient time for every one to get a look at everyone else's dot, one team member is randomly selected to make one helpful public announcement. After the announcement is made, each person returns to her/his private room. * If a person comes to know the color of her/his own dot s/he is to pick up a black or a white card corresponding to her/his now known dot. Then everyone returns to the large room. If anyone displays a card with the wrong color, the team is disqualified. After a time sufficient for every team member to again see the dot for every other member, and to see all the cards (if any), the members again return to the private rooms. The process described in the * paragraph above is repeated until everyone displays a color card. (Note that if any team member who is unable to deduce the color of her/his dot, after a time which that member feels is enough, s/he may intentionally tell some other person the color of the dot which in on that other person's back. This will immediately terminate the team's further participation in the contest.) The challenge is for each team to to have all of its members holding a card with the correct color as quickly as they can, that is with the fewest iterations of paragraph * above. The teams win prizes depending on the time it take for every member of the team to display a correct color card. The fastest team wins the largest prize. Assume that you are a member of a team, and you are selected to make the one public announcement. What is your announcement? SUGGESTION To avoid spoilers for some who are thinking about this puzzle, those with a solution they would like to post should postpone doing so for a few days. After a few days I will post my solution, and then others can do so if they like. I would be very interested to see the variety of solutions that people might post.