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MathNet 2012 Question 56

Math Olympiad Vault · MathNet 2012

Question 56

A box contains 105 black balls, 89 gray balls, and 5 white balls. Outside it there are enough white balls to repeat the following procedure until two balls remain in the box:
- Take two balls out without looking.
- If their colors differ, return the darker one to the box.
- Otherwise discard both and put a white ball into the box.

What can be guaranteed about the two remaining balls?

A) Both are white.

B) Both are gray.

C) Both are black.

D) Exactly one is black.

E) Exactly one is gray.