The question asks for the total number of participants in a tournament where everyone plays each other once. If 3 players fell ill after playing three matches each, that`s a total of 9 matches. These 9 matches must be subtracted from the total of 75, leaving 66 matches played by the remaining players.

Bearing in mind the formula for combinations in a group (n(n-1)/2), where n is the number of participants, is used to calculate the total number of matches in such a tournament.

Option 1: If there were 8 participants, they would have played 28 matches (8(8-1)/2), which is not enough.

Option 2: If there were 10 participants, they would have played 45 matches (10(10-1)/2), still not enough.

Option 3: For 12 participants, the number of matches would be 66 (12(12-1)/2), close but not including the 9 matches played by the ill participants.

Option 4: If there were 15 participants, they would have played 105 matches (15(15-1)/2), but after deducting the matches played by the ill participants (15-3) and recalcul