Katniss recieves the broth after kissing Peeta. Katniss takes this as a message from haymitch that says "If you kiss Peeta, you will get sponsors" So that is why the broth is sent, because haymitch is trying to send her a message. Hope this helped (:
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We do not know. It does not tell us. But Katniss thinks so. And FYI its Mockingjay, not hunger games
Because she was starving, and he wanted to help her. His mother had said to throw the bread at the pigs because Peeta had burnt it. instead he throws it to Katniss.
In the 74th annual Hunger Games, Katniss doesn't really seem to do anything to receive the gifts that Haymitch sends her. Haymitch watched The Hunger Games and observed what Katniss was doing and what exactly she needed and when she needed it. For instance, to gain the audience's attention and devotion for the "star crossed lovers of District 12", Haymitch sent Katniss broth to give to Peeta when he was in pain while he was in the cave to make the audience feel compassion for the couple.
Katniss is actually an aquatic plant that is also called Saggitaria. The seeds in the center of the flower of the plant are shaped like arrowheads. The plant gets its name from the Zodiac constellation Sagitarrius - or, "The Archer."