A problem from the Singapore Mathematical Olympiad has been travelling around the internet, since being shared on Facebook by Kenneth Kong. This site provides an easy way to work through the problem, to better understand the correct solution and how to solve the problem.
How to Use This Site
Click on one of the possible dates for Cheryl's birthday. Then you can follow the thoughts that Albert and Bernard have as they attempt to solve the problem. If one of the claims they make does not match up with the date you selected, then that claim will show up in red, and you can hover over it to see why it is incorrect.
Pick a possible day
Follow Albert and Bernard's Discussion
If Bernard heard 14, then he thinks it is July 14th or August 14th.
If Bernard heard 15, then he thinks it is May 15th or August 15th.
If Bernard heard 16, then he thinks it is May 16th or July 16th.
If Bernard heard 17, then he thinks it is June 17th or August 17th.
If Bernard heard 18, then he knows it is June 18th.
If Bernard heard 19, then he knows it is May 19th.
I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
I know Albert didn't hear May, since I might have heard 19, and would know it is May 19th.
I know Albert didn't hear June, since I might have heard 18, and would know it is June 18th.
If Albert heard July, he thinks it is July 14th or July 16th.
If Albert heard August, he thinks it is August 14th or August 15th or August 17th.
At first I don't know when Cheryl's birthday is, but I know now.
I know Bernard knows Cheryl's birthday is in July or August
I know Bernard didn't hear 14, because he wouldn't know if it is July 14th or August 14th.
If Bernard heard 15, he knows it is August 15th.
If Bernard heard 16, he knows it is July 16th.
If Bernard heard 17, he knows it is August 17th.
Then I also know when Cheryl's birthday is.
0/3
makes even Albert's first statement incorrect. Pick another date to try again.
1/3
makes Albert's first statement correct, but then neither Albert nor Bernard can correctly identify Cheryl's birthday from the information that they were given. Pick another date to try again.
2/3
allows Bernard to deduce Cheryl's birthday, but Albert does not have enough information to do so as well. Pick another date to try again.
3/3
is the only possible date for Cheryl's birthday that makes all three statements correct. Pick another date to see why it is invalid.
