Blog | frasergo.orghttps://www.frasergo.org/blog/2015-04-19T16:22:25+00:00BlogBirthdays, logic and honesty2015-04-19T16:22:25+00:00david/blog/author/david/https://www.frasergo.org/blog/2015/04/birthdays-logic-and-honesty/<p>A friend recently sent me the fun <a href="https://www.facebook.com/4sasmo">Singapore maths olympiad</a> <a href="http://bgr.com/2015/04/15/math-olympiad-singapore-cheryl-birthday-viral/" title="Hint: use logic">problem in which Albert and Bernard attempt to discover Cheryl's birthday</a>. As well as being full of mathematical knowledge, this implies some philosophical assumptions about knowledge and truthfulness. Here's a slightly expanded version I made up, incorporating the question of honesty:</p>
<p>Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:</p>
<ul>
<li>April 3, April 29, April 30,</li>
<li>August 10, August 11, August 12</li>
<li>September 3, September 29</li>
<li>December 3, December 10, December 12</li>
</ul>
<p>Cheryl then tells Albert and Bernard separately the month and day of her birthday respectively.</p>
<ul>
<li>Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.</li>
<li>Bernard: At first I didn't know when Cheryl's birthday is, but I know now.</li>
<li>Albert: Then I also know when Cheryl's birthday is.</li>
</ul>
<p>(pause)</p>
<ul>
<li>Bernard: Actually, I was bluffing when I said "I know now". It wasn't true.</li>
<li>Albert: Well now that Bernard's admitted that, to be honest, I was lying in the first place when I said that I knew that Bernard didn't know too... I didn't know that.</li>
<li>Bernard: Outrageous! Well, at least we both know when it is now (assuming we've been perfectly honest since the pause)</li>
<li>Cheryl: I can see I was wise not to tell you my birthday in the first place, you dishonest scoundrels. But to be perfectly honest, I don't know when my birthday is, and this was all a test...</li>
</ul>