The officers decided on the unusual tactic after the 17-year-olds, who have not been named, knocked on about 15 doors collecting sponsorship money in the North Ferriby area, claiming they were taking part in a charity event for Breast Cancer UK.
But the youths never had any intention of handing over the cash or taking part in the event, the police said.
Humberside Police interviewed one of the 17-year-olds, who was given a final warning with a condition that all three boys must take part in a specially designed event.
The officers told them they had to take part in the run and, between them, raise 100 to be donated to the cancer charity.
The trio, who are from Hull, completed the 10 mile route from Kirkella Police Station, over the Humber Bridge to Barton and back again, on Saturday.
PC Andy White from Kirkella Police Station said: "As a juvenile, we give them three chances.
"A young person can be given two reprimands and a final warning for relatively low level types of crime including anti-social behaviour, criminal damage and low-level assaults.
"These warnings are not criminal convictions but do stay on the person's record for five years or until they become 18 years old.
"If they continue their offending, the next time they come into contact with the police, they may be charged to court.
"When a warning is given to a child, we work with the parents and guardians to change their child's behaviour and we also work closely with the youth offending team at the council to ensure they are put on some sort of programme so they can be educated and learn by their mistakes.
"On this occasion, as the parents have been so disappointed by their children's behaviour and are all very pro-police, we decided to use this final warning as an opportunity to give the three lads a chance to earn back the money they obtained."
The officers invited some of the victims who paid the boys the money to be present at the start of the sponsored run, which was supervised by Detective Constable John Thompson, who is a keen runner.