The final exam in a class will either be in either March, April, May, or June. T

Question

The final exam in a class will either be in either March, April, May, or June. The professor indicates the possible dates:

• March: 15, 16, or 19

• April: 17 or 18

• May: 14 or 16

• June: 14, 15, or 17

Student A is given the month (but not the day) while student B is given the day (but not the month). The following conversation occurs:

A says: "I do not know when the final will be, but I know B does not know either."

B says: "At first, I did not know the date of the final, but now I know."

A says: "Ah! Now I know it too."

When is the final? Be sure to prove/justify every statement you make.

Explanation / Answer

After A says: "I do not know when the final will be, but I know B does not know either." :

If we look at the dates we observe that if April 18 or March 19 were final dates then B would have known it instantly because there are only one date with 18 and 19.If A knows this fact then he is either told May or June Month. Hence all the dates of April and March are eliminated.

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We are now left with dates of May and June only.

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After B says: "At first, I did not know the date of the final, but now I know.":

This eliminates May 14 and June 14 because If B know the exact date, it can’t be 14 as that will create ambiguity between May 14 and June 14.These two dates are eliminated.

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So, we are left with : May 16, June 15, June 17

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After A says  "Ah! Now I know it too." :

If A knows the date then it has to be May 16 because, in June there are two choices and A can’t be sure of his decision. If A is absolutely sure then answer is May 16 and all the june dates are eliminated.

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Hence answer is May 16.

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