Questions In Interview

Interview Question: The Birthday Problem

You and your colleagues know that your boss A’s birthday is one of the following 10 dates:

Mar 4, Mar 5, Mar 8
Jun 4, Jun 7
Sep 1, Sep 5
Dec 1, Dec 2, Dec 8

A told you only the month of his birthday, and told your colleague C only the day. After that, you first said: “I don’t know A’s birthday; C doesn’t know it either.” After hearing what you said, C replied: “I didn’t know A’s birthday, but now I know it.” You smiled and said: “Now I know it, too.” After looking at the 10 dates and hearing your comments, your administrative assistant wrote down A’s birthday without asking any questions. So what did the assistant write?



Strategy and Approach to Answering a Problem Solving Interview Question

If you get asked a problem solving question in an interview, remember that they are NOT looking for the RIGHT answer. They are evaluating the approach you use to think out and solve the problem. A strong candidate demonstrates the following:

  1. Evaluates and understand the scope of the problem
  2. Communicates assumptions
  3. Demonstrates quantitative analytical skills
  4. Answers the question that has been asked. You’d be surprised how many candidates get lost in the analysis and solve for a different question than what was asked.


How to Answer this Problem Solving Interview Question

Remember to evaluate and understand the question.  Don’t let the “he said, she said” part confuses you. Just interpret the logic behind each individual’s comments and derive useful information from these comments for your process of elimination.

Let D = the day of the month of A’s birthday, where D={1,2,4,5,7,8}

If the birthday is on a unique day, C will know the A’s birthday immediately. Among possible Ds, 2 and 7 are unique days. Considering that you are sure that C does not know A’s birthday, you must infer that the day the C was told of is not 2 or 7.

1) By process of elimination, the month is not June or December.

(If the month had been June, the day C was told of may have been 2;  if the month had been December, the day C was told of may have been 7.) Now C knows that the month must be either March or September. He immediately figures out A’s birthday, which means the day must be unique in the March and September list. It means A’s birthday cannot be Mar 5, or Sep 5.

2) By process of elimination, the birthday must be Mar 4, Mar 8 or Sep 1.

Among these three possibilities left, Mar 4 and Mar 8 have the same month. So if the month you have is March, you still cannot figure out A’s birthday. Since you can figure out A’s birthday, A’s birthday must be Sep 1.

3) Hence, the assistant must have written Sep 1.

Note: For this problem solving job interview question, there is an actual logical answer, however the interviewer will want to evaluate your thinking process. In answering the interview question, the lead up to your answer will be just as important as the actual answer itself.

For more problem solving, brain teasers, riddles, puzzles, logic job interview questions, please check our out Problem Solving Interview Section.


List of Problem Solving Interview Questions used by top firms (i.e., Microsoft, Google, IBM, etc.)