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Takeaway Time

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Since all the students who liked pizza also liked Chinese, and no student liked all three, we can just think about the remaining $25$ students.

Of these, $14$ liked Chinese and $16$ liked Indian. Since each student liked at least one of these, and there are a total of $30$ 'likes', $5$ students must like both Indian and Chinese.

This leaves $11$ students who liked Indian only.

This problem is taken from the UKMT Mathematical Challenges.