PA28 Instructor was told to follow the second PA28 on downwind by the Tower; when there were actually three PA28's on downwind. This results in a NMAC with the third PA28.

Narrative

On upwind in the traffic pattern we were instructed to follow second Warrior on downwind by the Tower. First sighted was off our right wing and second was one mile behind the first. We reported to Tower that the traffic was in sight and would follow as instructed. The traffic Tower meant was beginning with the second Warrior we had sighted and then the third behind it. This could have been from their sight as the correct order because the first Warrior we saw; to them; may have already been behind us from their viewpoint. This caused a near miss when turning downwind with the third Warrior. The third Warrior was 100 FT below us according to ASD Radar in the tower and evasive action was taken on the downwind. There were three Warriors on downwind; two of which Tower believed to still be in front of us with the third behind. This is what led to the confusion as all three were still ahead and to the right on downwind when we followed the second one in sight. A clarification of 'Traffic currently off right wing' or a more specific count of aircraft on the downwind may have helped in this situation. This would be similar to 'number two cleared stop and go' with the call of 'number four on downwind'.