Question

Bob, Jim and Mimi are sitting in the park and talking about the great birthday party Bob had recently. Suddenly, Bob asks: “Mimi, when is your birthday?” Mimi replies: “Let’s see if you can figure it out”.

Mimi takes a sheet of paper and writes the following dates on it:

April 18

April 19

April 22

May 20

May 21

June 17  

June 19

July 17

July 18

July 20

Then, she says: “One of these dates is my birthday. I will now tell Bob the month of my birthday, and I will tell Jim the day of my birthday”. So, Mimi whispers the month in Bob’s ear, and she whispers the day in Jim’s ear. Mimi says: “without saying out loud what I just whispered in your ears, do any of you know my birthday?” Bob says: “I don’t know, and I know that Jim doesn’t know either” Jim says: “At first I didn’t know, but now I know”. Bob says: “Now I know too”. What is Mimi’s birthday?

Answer 1

Given the data,

Day 17 is for June and July

Day 18 is for April and July

Day 19 is for April and June

Day 20 is for May and July

Day 21 is for May

Day 22 is for April

Bob says: “I don’t know, and I know that Jim doesn’t know either”. So, the month will not be April and May. Because the day 21 and 22 are unique and Jim would be able to identify the birthdate. As, Bob is confident that Jim also does not know, the months whispered to Bob are not April and May.

Hence the possible months are June or July.

Now, Jim says: “At first I didn’t know, but now I know”. The dates for June and July are,

June 17  

June 19

July 17

July 18

July 20

If now, Jim knows then that day is unique in June and July month dates. So, the possible birthdates are June 19, July 18 or July 20.

Now, Bob says: “Now I know too”. Bob Jim knows then that month is unique for the remaining birthdates June 19, July 18 or July 20. The unique month is June.

Thus Mimi's birthdate is June 19.