What is a stalemate in The Hunger Games?

Answer 1

if katniss shoots cato to kill him, cato will take peeta with him into the mutts below. in response to this, peeta has katniss shoot cato's hand.

You might be talking about why Cato hates Katniss if so its because Katniss and Peeta took the croward away from them when they road in on their charriots at the begining when Katniss gets her name "The girl on fire"

Answer 2

When Cato has Peeta in a headlock at the Cornucopia, and Katniss can't shoot him without Cato snapping Peeta's neck but he can't snap Peeta's neck without being shot by Katniss.