From the Super Mario Wiki
Super Mario series
Super Mario 3D Land
Boomerang Flowers first appear in Super Mario 3D Land. They can be found lying on the ground, inside of ? Blocks, and after defeating some Boomerang Bros. After obtaining it, Mario can throw a boomerang to defeat enemies and reach items from a far distance. However, Mario can only throw one boomerang at a time and must wait for his first boomerang to return or disappear before he can throw another. This power-up first appears in World 5-1.
Super Mario 3D World
The Boomerang Flower reappears in Super Mario 3D World and has the same function. The color of the boomerang changes depending on which character threw it.
Mario Golf: World Tour
The Boomerang Flower appears in Mario Golf: World Tour as an item that the player may collect during matches. It increases dramatically the fade or draw of a character.
Mario Kart 8
The Boomerang Flower appears in Mario Kart 8 as a new item to the Mario Kart series. It allows the player to throw a boomerang up to three times, hitting any karts in the way going forward before coming back to the player. It will also hit the opponent on the way back if the player misses the first time. When the player throws the boomerang, his/her item slot will become empty and will show the boomerang after it returns to the player, so if the boomerang is thrown and the player runs into an item box, the boomerang will come back to the player and disappear. If a player manages to catch the boomerang as it is coming towards them by pressing R on the Wii U GamePad, they will take the item and its remaining uses from the attacker. The height of the vehicle affects the height of the boomerang's throw, which may result in low-down vehicles being too low to be hit by the boomerang thrown by a character in a tall vehicle.
Mario & Luigi: Paper Jam
While Boomerang Flowers do not physically appear in Mario & Luigi: Paper Jam, one is used as the logo for the Boomerang Rank.
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