Singapore logic puzzle
First, you have to figure out what Albert knows that Bernard doesn’t. Cheryl gave the pair 10 possible dates. The combinations are made up of four possible months and dates falling between 14 and 19. Only 18 and 19 appear once across the 10 combinations. If Bernard was told either 18 or 19, he would know Cheryl’s birthday — either May 19 or June 18. Albert says he doesn’t know when Cheryl’s birthday is, but neither does Bernard. If Cheryl had told Albert she was born in either May or June, it would be possible for Bernard to know when her birthday is (assuming she told him either 19 or 18). If Bernard can’t know Cheryl’s birthday with his information alone, we know Cheryl told Albert she was born in either July or August.
After Albert says his piece, Bernard announces he now knows when Cheryl’s birthday is. At this point, he has also been able to deduce the months down to July or August. From the potential dates in those two months, only 14 appears twice. To know Cheryl’s birthday, Bernard must have been told a number other than 14.
Albert then announces he also knows Cheryl’s birthday, having eliminated two months and the number 14. This leaves him with three potential dates: July 16, August 15 and August 17. If Cheryl had told Albert August, he would not know because he would still be missing the date — either 15 or 17. Cheryl must have told Albert July, leaving him with only one possible date to celebrate his new friend’s birthday: July 16.
Cheryl’s birthday is on July 16
If it was May => Albert cant say the first statement, as if the day was 19, Bernard will know the birthday for sure.
If, it is was June => Same is the case with 18th.
If, it is in July => Albert can say the first statement.
If it is in August => Albert can say the first statement.
Now after hearing first statement, Bernard can clearly figure out that the month of birthday is either July or August.
So, if the day was 14 => It can be July 14 or August 14 =>as bernard know now, it is not possible
If the day was 15 => It can be Aug 15
If the day was 16 => it can be July 16
If the day was 17 => it can be Aug 17
Only three days possible are Aug 15, July 16 or Aug 17, bernard knows the day so he know the birthday.
From the third statement, Albert knows the birthday as well, so it can only be July 16, as if the month was Aug, Albert can not figure it out.
Thus the Cheryl’s birthday is on July 16.
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