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.
I am not sure that is true. If albert knows bernard doesn't know the day at the beginning, it can't be june since the number 18 would be uniquely identifiable as june 18 for bernard from the beginning.
Albert does not know the day, he knows the month. Alberts statement eliminates all June and May dates because he says he "Know thats Bernard doesn't know" before Bernard says he didn't know.
Your second solution depends on interpreting the "Albert knows Bernard doesn't know" to mean that Bernard told (or otherwise signalled to) Albert that he doesn't know, rather than Albert deducing that Bernard couldn't know.
There was a detailed rebuttal of this interpretation by the folks who set the original question.
But it is easy to claim "that's not what I meant!" Actually being precise about what you mean is fiendishly difficult. I recommend Imre Lakatosh's excellent book on proofs "Proofs and Refutations" - its short, and thoroughly dismantles the early 20th century ideas that math is somehow a precise conceptual structure independent of language ambiguities.
Or put another way: with enough eyeballs, all language is ambiguous.
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.
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.
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.
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.
I haven't done logic problems in a long time, so I may have erred and would welcome alternative interpretations.
The island puzzle, for those who haven't seen it yet.
I think that one is much more difficult because the problem is stated in a way that makes the readers think she has much less information that is actually given. The birthday problem has no trick phrasing in it.
Well, maybe a little tricky. You'd get stuck if you tried to reason from four months and six days. This would be a likely mistake if the problem were read aloud with the list of dates as "May 15, 16, and 19, or June 17 and 18..."
Recognizing that Albert and Bernard are both working with sets of 10 elements each -- one for each possible date -- then it becomes a simple graph problem.
Write a chart with rows labeled months and columns labeled days. Put a mark on each possible date. Albert circles one row and Bernard one column. Albert says none of the marks in his rows are the only marks in their columns, so draw a line through the columns with only one mark and the rows that intersect at that mark. Bernard says there is only one mark in his column after eliminating the row, so draw a line through the columns with more than one mark. Albert says there is only one mark in his row, so draw a line through the row that still has two marks in it. The only one left is July 15.
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.
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.
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.
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.
15 comments
[ 5.3 ms ] story [ 40.0 ms ] threadThere was a detailed rebuttal of this interpretation by the folks who set the original question.
But it is easy to claim "that's not what I meant!" Actually being precise about what you mean is fiendishly difficult. I recommend Imre Lakatosh's excellent book on proofs "Proofs and Refutations" - its short, and thoroughly dismantles the early 20th century ideas that math is somehow a precise conceptual structure independent of language ambiguities.
Or put another way: with enough eyeballs, all language is ambiguous.
https://news.ycombinator.com/item?id=9375643
https://news.ycombinator.com/item?id=9367438
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.
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.
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.
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.
I haven't done logic problems in a long time, so I may have erred and would welcome alternative interpretations.
The island puzzle, for those who haven't seen it yet.
I think that one is much more difficult because the problem is stated in a way that makes the readers think she has much less information that is actually given. The birthday problem has no trick phrasing in it.
Well, maybe a little tricky. You'd get stuck if you tried to reason from four months and six days. This would be a likely mistake if the problem were read aloud with the list of dates as "May 15, 16, and 19, or June 17 and 18..."
Recognizing that Albert and Bernard are both working with sets of 10 elements each -- one for each possible date -- then it becomes a simple graph problem.
Write a chart with rows labeled months and columns labeled days. Put a mark on each possible date. Albert circles one row and Bernard one column. Albert says none of the marks in his rows are the only marks in their columns, so draw a line through the columns with only one mark and the rows that intersect at that mark. Bernard says there is only one mark in his column after eliminating the row, so draw a line through the columns with more than one mark. Albert says there is only one mark in his row, so draw a line through the row that still has two marks in it. The only one left is July 15.
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.
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.
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.
Therefore July 16.
can't be any of the months with unique numbers, so May and June are out
It can't be 14th therefore as you are still confused between July and August
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
edit - BBC baffles world by claiming basic logic puzzles baffle world.
edit 2 - This attitude to maths in news reports is utterly poisonous. The papers publish more difficult sudokus daily in their puzzle section.