What are Sets? - Definition & Examples

$$\text{Give Me a Sign}$$

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*This question is a variation of a teaser asked in the Singapore and Asian Schools Math Olympiad.

It’s Chinese New Year! It is the year of the Dog. Similar to horoscope signs, there are also 12 Chinese Zodiac signs and each zodiac sign is said to have certain personality traits. While a person’s horoscope is dependent on their birthday, their Chinese Zodiac sign is dependent on their birth year. Alex decides to give a brainteaser for people to figure out what his horoscope and Chinese Zodiac signs are. He reduces all of the possible combination down to these 10 (in green). Only one combination is true.

Tori already knows the answer. To help Christine and Liza out, she told Christine Alex’s Chinese Zodiac sign and told Liza Alex’s horoscope sign. Christine and Liza are not allowed to share that information. However, they did figure out a way to find the answer. This is the conversation they had:

Christine: I don’t know what Alex’s combo is, but I know that Liza doesn’t know either. $\\$ Liza: At first I didn’t know, but now I do. $\\$ Christine: Then I also know!