My logic for this puzzle goes as follows:<p>1) Albert knows Bernard cannot know the answer immediately. As 18 and 19 are days that only appear once, the month must not contain those dates, so May and June are eliminated.<p>2)Bernard is able to identify the month based on knowing it can't be june or may and based on his date. Therefore Bernard cannot have had the number 14. He must have 15,16, or 17.<p>3) Knowing it is 15, 16, or 17 uniquely identifies the date for albert. Since august has 2 options left, it must be july, and the only date available is July 16.<p>This is a tricky problem, but it is one that is fairly straightforward to approach step by step. Definitely appropriate for advanced students at age 15. The problem reminds me of the question about how many people on an island have blue/brown eyes.<p>I haven't done logic problems in a long time, so I may have erred and would welcome alternative interpretations.
July 16th<p>can't be any of the months with unique numbers, so May and June are out<p>It can't be 14th therefore as you are still confused between July and August<p>If it was 15 or 17, then there would still be confusion about which, so Albert must have been told July and Bernard must have been told 16<p>edit - BBC baffles world by claiming basic logic puzzles baffle world.<p>edit 2 - This attitude to maths in news reports is utterly poisonous. The papers publish more difficult sudokus daily in their puzzle section.
I think there are two solutions. The video in the link gives one, the other is June 17. Supposing Albert knows the day, his statement eliminates June 18 and May 19. Bernard claims to know the answer, which can only be June 17. Albert does the same logic and reaches the same conclusion.
1. Albert has July, so he knows all the days Bernard could have been given have duplicates. Thus, he knows Bernard doesn't know the birthday yet.<p>2. Bernard hears this and knows Albert is holding on to either July or August. He holds a number that is unique within these 2 months. That is why he now knows the birthday.<p>3. Albert now knows that Bernard knows, and thus has a day that is unique between July and August. Which means it cannot be 14.<p>4. So among July 16, August 15, and August 17, the only way Albert can know for sure is if he is holding on to July.<p>Therefore July 16.