The series of unprovoked attacks happened in broad daylight Saturday afternoon between Massachusetts Avenue and Trowbridge Street.
In this first incident, according to a Cambridge police report, a man told officers he was walking towards Central Square when the suspect walked "directly towards him."
Update: Victims Of Attacks Speak Out
"He stepped to his left and the suspect mirrored that move. He stepped to his right and the suspect moved into his path once again. When the suspect was close enough, he punched (the victim) at least twice in the eye with a closed fist, knocking him to the ground," the report stated.
The attacker then took off towards Harvard Square and hit two more men.
WBZ NewsRadio 1030's Carl Stevens reports
Police Seek Sucker Punch Suspect
In the third incident, the suspect sucker punched the victim in the head, right after he left BoConcept furniture. That attack was captured on the store's surveillance video.
The store owner told WBZ-TV he actually helped victims number two and three.
"We ran out to help (the third victim), brought him inside. This guy had a bruised ear and cheekbone. He was going ballistic. Then the previous victim came in. We helped him, too. He had a big fat lip," BoConcept owner Anthony Goodh said Monday.
Minutes earlier, the suspect had apparently been inside the Garden at The Cellar Restaurant, where he allegedly tried to punch the chef, Brandon Arms.
"Brandon was out here, and (the suspect) took a swing at him. Brandon shoved him away and started chasing him. He ran a little faster. I believe he chased him that way," the restaurant owner, Steven Kapsalis, told WBZ.
There has been no arrest yet. One of the three victims had to be taken to a hospital to be treated for minor injuries.
Police have described the suspect as tall, black, in his mid-twenties wearing a black winter coat, a dark knit hat and blue jeans.
Investigators do not believe this was an example of the so-called "knockout game," where people intentionally commit assaults, videotape them, and post them online.
"We believe at this point, that these assaults were not a case of "Knockout", but a situation where an individual who was either under the influence or suffering from some type of mental illness was responsible for the assaults," Cambridge Police Deputy Superintendent Jack Albert told WBZ in an email.
MORE LOCAL NEWS FROM CBS BOSTON
for more features.