The damage was caused to three takeaways in Salvington Road, Worthing, in the early hours of Friday, January 18, according to police.
A spokesman said: "We are asking anyone who may have information about this incident to call us quoting reference 112 of 18/01/2019."
Oz's Charcoal Grill, Hot Spot Indian Takeaway and King Pizza and Kebab were all affected.
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