The envelope and the number

Logic Level 4

Pi Han has written down a perfect square between 1 to 300 inclusive. Calvin wants to know the integer, and is allowed to ask "yes/no" questions to determine it. Pi Han would immediately answer the question, and then Calvin can use that information to ask his next question. As a point of pride, Calvin would not ask questions to which he already knows the answer. Calvin asks the following questions:

  1. Is it less than 100?
  2. Is it even?
  3. Is it 2-digit?
  4. Is the second digit from the left a 6?

At this point, Calvin declares that he knows the answer. However, he turns out to be incorrect because Pi Han gave the wrong answer to each of the 4 questions!

What is the number in the envelope? If you think it cannot be uniquely determined, enter 0 as your answer.

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Clarification: Before the questions are asked, Calvin knows that Pi Han wrote down a perfect square between 1 and 300 inclusive.

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