A 24-year-old woman held on to her handbag when a man tried to rob her in the centre of Brighton on Monday (21 January).
The man approached her in Pavilion Gardens at about 6.20pm, threatened her and demanded money.
After she refused to give him any money, he tried to grab her handbag but she refused to let go of it.
Sussex Police said: “He then turned and walked away and was last seen heading towards the centre of the Gardens.”
The force also received complaints from five other people saying that a man was acting strangely in Pavilion Gardens.
They said that, at about the same time, he was approaching people, demanding money and growling at them.
No one was injured in any of the incidents and nothing was stolen.
Detective Constable Chris Bishop said: “We believe this to be the same man on each occasion and inquiries are ongoing in order to try to identify him.
“He is described as white, in his late teens to early twenties, of slim to medium build, around 5ft 7in to 5ft 11in tall, with a southern or London accent.
“He was wearing either a dark balaclava or knitted hat and scarf that he used to cover his face, a dark jacket made by Schott, dark gloves and dark jeans.”
He urged anyone who saw or was approached by the man or who knows who he is to call Sussex Police on 101 or the independent charity Crimestoppers anonymously on 0800 555111.
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