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A man found walking around Gravesend with a facial injury was taken to a London hospital for treatment.
Police are now appealing for witnesses to help them establish what happened.
The man was discovered between 5pm and 6.22pm on Sunday, May 28 walking in Arthur Street from the direction of Darnley Road.
He was subsequently taken to a London Hospital for treatment to facial injuries.
Officers have carried out a number of inquiries, including checking for forensic evidence, speaking with people who saw the man walking in the street and talking to residents in the area.
A spokesman said: "Officers remain keen to establish the full circumstances of how this man came to be injured and are asking for people with information, that are yet to speak with them, to get in contact."
Anyone with information can call Kent Police on 01474 366149 quoting XY/24825/17. Alternatively contact Kent Crimestoppers anonymously on 0800 555111.