PROVIDENCE — For months a burglar plundered the East Side, stealing jewelry, electronics and cash. The police knew they had a problem, but they were unable to catch him.

And then one man whose cell phone was stolen in a housebreak took matters into his own hands. He needed that phone in particular because of the list of phone numbers stored in its memory.

So he called his cell phone, talked to the person who had it, and arranged to buy it back.

And thus a trap was laid.

A police detective went to the buyback appointment in his place, and an acquaintance of the burglar was taken into custody. That arrest led to the alleged burglar himself, Bruce McKenzie, 18, of 22 Leah St., in the Mount Pleasant section of Providence, who this week was charged with 16 crimes and is now cooling his heels at the Adult Correctional Institutions.

The police say the arrests have solved housebreaks that occurred from January through this month in which tens of thousands of dollars in loot was taken — sometimes because unlocked doors and windows made it easy for the thief.

A continuing investigation is expected to solve at least 15 more housebreaks, detectives say.

McKenzie “felt he was teaching people a lesson,” that they should not leave their houses unsecured, said Detective Angelo A’vant. In a gesture that has made the investigation much easier, according to A’vant, McKenzie took detectives on a tour of the houses he had allegedly struck and related some of things he had learned while pawing through people’s belongings.

“He had a vivid memory. He could remember names, what [the homeowners] did for a living,” how he had gotten inside and the interior layouts of the houses, A’vant said. More than once, according to the detective, McKenzie had returned to the scene of a crime, going back for something he had not been able to carry away the first time.

Two of the housebreaks had not been reported to the police — in one case because the victim had suffered an unrelated personal tragedy and was preoccupied, and in the second case, because two college students did not realize their laptop computers were missing, the police said.

Once there was a scary confrontation: on April 28, when a sleeping house sitter awoke to the presence of an intruder at 3 a.m. in an apartment at 683 Hope St. The intruder hurriedly left.

On another occasion, according to a police report, McKenzie got in and out of an apartment at 23 James St. while a man was in the shower.

The general modus operandi, according to the police, was to enter in the daytime, usually between noon and 4:30 p.m. when people were likely to be out: McKenzie probed first for an unlocked entry point, and if there was none, kicked in or pried open a door or window.

His take was lucrative, including individual jewelry pieces worth $10,000 to $15,000. But his lack of sophistication, the police pointed out, prompted him to sometimes spurn valuable items in favor of the less valuable. The goods were sold on the street or to a pawn shop — he did not use his own name in a pawn — for a fraction of their retail value, according to A’vant. But it netted McKenzie $2,000 to $3,000 a week, he said.

The case was cracked after David Bielory, 29, of 23 Sarah St., had his Nokia cell phone stolen, along with a slew of jewelry, $300 and a piece of computer equipment on April 30. The police say McKenzie got in through the garage door.

A friend tried to call Bielory at his cell phone number and was surprised to reach a stranger. A series of conversations then ensued in which the friend and then Bielory dickered to buy back the phone. When a meeting was arranged, Detective Robert DeCarlo went in Bielory’s place.

The acquaintance, who was not charged, said he got the phone from McKenzie. When the police arrested McKenzie, he allegedly had 10 bags of crack cocaine with him.

In a twist, A’vant said, the acquaintance said he had meant to throw away the SIM card from Bielory’s phone. If he had done so, Bielory and his friend never would have been able to make contact. A SIM card is a portable memory chip that makes a hand-held device identifiable to a particular phone number and holds other data such as the owner’s bank of phone numbers.

Maj. Stephen Campbell, commander of the police Investigative Division, commended Bielory for his cooperation with the police and Detective Sgt. Daniel Gannon, who is leading the investigation, for getting results. A few of the stolen goods have been recovered, but most were sold.

McKenzie is charged with 15 counts of breaking and entering, one count of burglary and one of possession of cocaine, all of which are felonies. Burglary is a distinct crime, defined as a nighttime break into an occupied residence, and carries a heavier penalty than breaking and entering.

He appeared Tuesday in District Court, where pleas to felony counts are not accepted. Judge Michael A. Higgins set bail at $10,000 with surety on the drug charge and $25,000 with surety on the 15 breaks. The suspect was held without bail on the burglary.

gsmith@projo.com