The solution, officials said, will be to open the gates at entrances for the R train shortly after midnight on Monday and hope that only R train riders find their way through. There will be no other measure taken to prevent riders on other lines from taking advantage.

The Cuomo administration predicted that few riders would seek an undeserved free ride.

The free-for-some (and perhaps all) began Friday, when Mr. Cuomo announced the proposal, calling it “a thank you to the M.T.A. riders” whose service was disrupted “for taking the hardships of the storm in stride and for their understanding in the months since.”

Later in the day, the governor’s office appeared mindful of the plan’s potential hiccups. A spokesman for the governor said at one point on Friday that to avoid logistical hurdles, fares would be free in Brooklyn only along the southern tail of the R train, which includes few transfers between Bay Ridge-95th Street and Union Street.

The spokesman later clarified that the train would be free for all R train riders, adding that the transportation authority was working on an “implementation plan for those stations” where transfers could allow anyone to ride without paying. But some possible solutions — a temporary barricade or using security personnel to ask riders which train they were seeking — were perhaps unworkable. There are an estimated 65,000 daily R train riders in Brooklyn and 30,000 on the A train in the Rockaways. The authority has said that its average fare — accounting for those with unlimited-ride MetroCards and other discounts — is $1.76, meaning that the idea will cost about $167,000 even before including other Brooklyn passengers who might ride for free.

The offer is far less complicated for affected A train riders, who were missing much of their line until last spring. The administration and the authority said on Sunday that the gesture remained a worthy acknowledgment of their hardships and those faced by R train riders, whose tunnel connecting Brooklyn and Manhattan could be closed for repairs until next fall.