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The man, described as being of Pacific Islander appearance, threatened the women with the weapon while demanding money.
Police said he ran from the scene without any cash.
On the same night just minutes later, another woman was threatened with a knife on Houston Road in Kensington.
Police said the man ran from the scene when he was startled by a nearby resident.
He was seen running towards Anzac Parade in Kingsford before boarding the 3910X bus to Maroubra, where he threatened a fourth person with a knife and demanded money.
No injuries were reported during the incidents.
The man depicted in images released by police is described as being of Maori/Pacific Islander appearance, with black hair.
He is shown wearing a black hoodie and black tracksuit pants, with a blue mask.
Police are appealing for any witnesses or anyone who may have information about his identity to contact Eastern Beaches Police Area Command.