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AMC8 2027 - Self-practice Set 5 Question 8

AMC8 · AMC8 2027 - Self-practice Set 5

Question 8

Three students stand in a line. The last student can see the first two, the middle student sees the first, and the first sees no one. A teacher selects their hats from five hats: two black and three white. No student sees their own hat or the two unused hats.
The last student says, "I do not know." The middle student also says, "I do not know." Hearing this, the first student says, "I know." All three are excellent reasoners. Which conclusion is correct?
  1. The first student wears white
  2. The first student wears black
  3. Exactly two students must wear black
  4. Exactly two students must wear white
  5. The second student wears white