A 91-year-old woman had skin torn off the back of her hand when a robber ripped a bag from her grasp.
With blood pouring from the wound, the 91-year-old staggered to a neighbour's flat for help.
She was taken to hospital to repair a large flap of skin and she was detained overnight.
The robbery happened in Clarendon Road, Hove, just after 4.30pm on Saturday.
Police think the mugger may be the same man who robbed 92-year-old Millie Kershaw last month.
The victim spent the afternoon with a friend and walked from Hove railway station to her flat in Livingstone House. She was at the communal front door when the attacker pounced.
She tried desperately to hang on to her black silk-cloth bag, containing her purse, £14 and false teeth.
The bag's handle cut into the back of her hand as the mugger prized it free and fled.
The victim, described as sprightly, broke down in tears as she was giving police details.
Detective Constable Dick Bidmead said: "She is an incredibly brave lady and tried extremely hard to keep hold of her bag."
The robber was 6ft, slim, in his late 20s and wore a blue-white baseball cap.
Another woman was robbed of her tanned-coloured shoulder bag as she was getting into her car in nearby Conway Street, Hove, at 10pm on Friday.
She lost her mobile phone and cash. She told The Argus: "These people are absolute cowards, especially those who pick on elderly women."
Her attacker wore a dark hooded sweatshirt with the hood up and baggy jeans.
Mrs Kershaw, 92, suffered a broken hip and wrist when a mugger grabbed her bag in Hamilton Road, Brighton.
She is recovering at the Brighton General Hospital.
All three robberies happened near to Brighton or Hove railway stations.
DC Bidmead said: "We are keeping an open mind whether the weekend's attacks were carried out by the same culprit."
Witnesses should call Brighton and Hove CID on 0845 6070 999 or Crime-stoppers on 0800 555 111.
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