Cheryl's birthday

I've now seen that there are two answers

I got August 17 and I think that's a better answer. My reasoning was and is this:

Step 1: A knows the month, B knows the date

Step 2: A deduces that B doesn?t know the answer just by having been told the date.

Step 3: therefore the date cannot be 18 or 19, since those only occur once each and so if B had been told either of those dates, he would know the month too.

Step 4: A tells B that he himself doesn?t know, but he knows that B doesn?t know either.

Step 5: this enables B to make deductions about the month. He can now rule out June, since only two dates have been given for June and B knows it can?t be one of them (June 18) and he knows that A knows that too. Therefore B now knows that A cannot have been told June (since otherwise he would know that it was June 17, but he has said he still doesn?t know). (This is where I part company from the July 16 people. They believe that you can eliminate May as well as June, reasoning that Bernard must know that Albert wasn?t told either of the months with 18 and 19 in them. I think this is false. Eliminating 18 and 19 only tells Bernard that it can?t be June. It could still be May, since taking out May 19 still leaves May 15 and 16.)

Step 6: having ruled out June, B is now left with May 15 and 16, July 14 and 16, and August 14, 15 and 17

Step 7: that immediately enables B then to say that he now knows the answer. This means that B can now know the answer simply from (a) knowing that the month can?t be June, and (b) knowing the number.

Step 8: therefore the number must be a unique number in the remaining numbers (or, if you prefer, a number which was previously not unique but has become unique since the elimination of June)

Step 9: therefore the answer is August 17, since 17 is the only remaining unique number (now that June 17 has been eliminated)

Posted By: Old Git, Apr 15, 12:26:23