Hmm, let's see:
Albert knows the month, so knows that it isn't one of the dates with unique days. (This implies that the month must be July or August.)
By announcing this fact, he tells Bernard that the month is either July or August.
Because this gives Bernard the information he needs to know the correct date, this implies that the day can't be one which is common to July and August. This means that the day isn't the 14th (so may be 15, 16 or 17).
Albert knows the month, and this gives him the correct date. This means the month can't be August, as there would still be two possible days.
The correct date is therefore July 16th?
To me that's a *hard* 12+ question, not year 5. But Singaporean children may be better at logic problems simply through merit of not being western, or else year 5 means something different there. It certainly means something different here to what it did when I was in year 5.
Hmm, let's see:
Albert knows the month, so knows that it isn't one of the dates with unique days. (This implies that the month must be July or August.)
By announcing this fact, he tells Bernard that the month is either July or August.
Because this gives Bernard the information he needs to know the correct date, this implies that the day can't be one which is common to July and August. This means that the day isn't the 14th (so may be 15, 16 or 17).
Albert knows the month, and this gives him the correct date. This means the month can't be August, as there would still be two possible days.
The correct date is therefore July 16th?
I have a different answer, and am probably wrong...
I don't see how you can eliminate May at the first stage. While one of the three May dates has a unique day, the other two are not (15, 16).
My probably incorrect logic led to August 17th.
1. Albert in knowing that Bernard cannot initially find a solution can eliminate May 19 and June 18 (unique days) as well as the (unknown to us and Bernard) months he was not given by Cheryl.
2. Bernard in knowing that Albert has not found a solution at stage 1, can eliminate June since if it was, Albert could have deduced June 17 as the only possible day. Of the options left, the 14th, 15th and 16th all have two possible months. Only the 17th has a single month left (August), so that is the only date he could have been given to have found a solution at stage 2.
3. Albert following the logic above can come to the same conclusion.
I don't see how you can eliminate May at the first stage. While one of the three May dates has a unique day, the other two are not (15, 16).
One is enough. If Bernard had '19', then he'd know the full date. Albert knows that Bernard doesn't know the full date, *because* he knows the month isn't May or June.
One is enough. If Bernard had '19', then he'd know the full date. Albert knows that Bernard doesn't know the full date, *because* he knows the month isn't May or June.
I must be being dense here, but I still don't get...
Why does a unique date in May (19th) rule out the other two May options?
Or working backwards from your answer, Albert has been told July, so knows that Bernard must have either a 14 or a 16. Bernard has been told 16, so knows that Albert must have either May, or July. I don't see how either could deduce the correct date in that situation.
It rests on the the interpretation of the first line "I don't know when Cheryl's birthday is but I know that Bernard does not know" as meaning "I don't know when Cheryl's birthday is but I know that it would be impossible for Bernard to deduce it at this stage". I had been interpreting it as "I don't know when Cheryl's birthday is but I know from Bernard's lack of declaration of the date that he does not know".
I guess the difference in interpretation is one of deductive vs inductive reasoning. Ultimately slightly unsatisfying as the difficulty in answering it was largely due to ambiguity in the wording of the question.
(Edit: Or basically what Owen61 says in Biggsy's post)
Goes like this
Label the prisoners A, B. C with C being the one wearing the blindfold
As there are only 2 red hats if either A or B can see 2 reds they would know that their own hat was white - A and B's statements indicate this is not the case
What A and B see therefore is either 2 white hats or one red and one white In either case C can identify his own hat as white
If A and B are unsure because they can see 2 whites then C's hat is white
If A or B can see a white and a red then it can't be C with the red as if B can see a red hat and a white hat after A has passed he would know his own hat was white
e.g. A white, B white C red
A sees a white and red and is unsure B sees a white and a red and knows his own hat can't be red as A would not have passed and therefore knows he is wearing white. As B passes we know that that combination is disallowed,
All other combinations have C wearing white