In a world where every human has a small, invisible dragon perched on their shoulder that becomes heavier or lighter based on the truthfulness of their statements, three friends Ambika, Beom, and Chika are trying to figure out who ate the last piece of cake. They agree to each make a statement and use the weight shifts of their dragons to deduce who the cake-eater is. Ambika says, "I didn't eat the cake," and her dragon remains neutrally buoyant. Beom says, "I think Chika ate the cake," and his dragon becomes slightly lighter. Chika says, "Beom always lies about cake," and her dragon gets considerably heavier. Assuming all three friends are aware of how their dragons react to truths and lies, what can Ambika and Beom deduce about who ate the cake? Provide a brief response.
Ambika's dragon remains neutrally buoyant after her statement, which suggests that her claim about not eating the cake is true. Beom's dragon becomes slightly lighter which indicates that there's some untruthfulness in his statement. Since Beom did not directly say he didn't eat the cake and only expressed a belief about Chika eating it, the slight change in weight implies that Beom may not be entirely sure of Chika's guilt but is not outright lying either; there is doubt in his statement. Lastly, Chika's dragon gets considerably heavier, showing that her statement about Beom always lying about cake is a significant lie.

Given the reactions of the dragons, Ambika can be confident she did not eat the cake, and now suspects that Beom's statement wasn't entirely truthful. Beom knows that he wasn't telling the whole truth because he wasn't sure of Chika's guilt; however, Chika's heavy dragon reveals that she lied about his honesty.

Thus, Ambika and Beom can deduce the following: Ambika did not eat the cake for certain since her dragon did not change in weight; Beom might not know who ate the cake but himself has not been ruled out since his dragon got lighter when casting suspicion on Chika; Chika likely ate the cake since she told a considerable lie regarding Beom and his tendency to lie about cake, as indicated by her dragon's significant weight increase. Hence, the most logical deduction is that Chika ate the cake.