Answer: Tuesday Teaser #30
This puzzle relies on simple logic, so let’s go through the statements step by step and see what they tell us.
Tom said: “If I don’t know, then Jerry definitely doesn’t know either.”
Jennifer told Tom the month in which she was born. Tom then asserts that Jerry cannot possibly know at this stage. If Jerry were able to tell the exact date, it would be because the day which he was told is unique among the 10 possibilities (remember that Jerry knows the day but not the month). Tom’s statement removes the possibility of a unique day, so the month he was told cannot contain a unique day. The unique days are the 2nd (December) and the 7th (June), so Tom is actually telling us that the birthday is not in December or June.
Jerry then said: “I didn’t know in the first place, but I know now.”
Jerry has used the above logic to narrow it down to the dates in March or September. The day he was told is now unique among those remaining possibilities and allows him to know the exact date for sure. This means that we can rule out March 5th and September the 5th and means that the date is either March 4th, March 8th or September 1st.
After hearing what Jerry said, Tom said: “Ah, then I know as well.”
Having narrowed down the list to three possibilities as above, Tom can now use the month he was told to determine the exact date. Given that there are two remaining dates in March and only one in September, for Tom to know for sure, the month he was told must have been September.
Therefore we conclude that Jennifer’s birthday is September 1st.
