From the Super Mario Wiki
Super Mario Bros. 3
Red Paragoombas make their first appearance in Super Mario Bros. 3 as a weaker form of Paragoombas. Their only method of attack is to hop along the ground, attempting to run into Mario or Luigi. To defeat them, the player must jump on them once to rid them of their wings and again to defeat them. Unlike their yellow counterparts, none of the levels show them wingless first.
Super Princess Peach
Red Paragoombas serve the same purpose in this game. A variant, the Mad Red Paragoomba, also appears. This species can cling to walls, allowing them to walk across high ledges without falling off the edge.
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