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<blockquote data-quote="Hawkman" data-source="post: 445097" data-attributes="member: 23715"><p>How the Logic Works (Example with k = 2 Muddy Children: Alice and Bob)</p><ol> <li data-xf-list-type="ol"><ul> <li data-xf-list-type="ul"><strong>Round 1:</strong><ul> <li data-xf-list-type="ul">Alice sees that Bob is muddy. She thinks: <em>"If I am clean, then Bob is the only muddy child. Bob sees no other muddy children, so Bob should realize he is muddy and step forward immediately."</em></li> <li data-xf-list-type="ul">Bob looks at Alice and thinks the exact same thing.</li> <li data-xf-list-type="ul">When the parent asks the first time, <strong>neither Alice nor Bob steps forward</strong>, because each is waiting to see if the other moves. </li> </ul></li> </ul><ul> <li data-xf-list-type="ul"><strong>Round 2:</strong><ul> <li data-xf-list-type="ul">Alice sees Bob <em>didn't</em> step forward on Round 1. She reasons: <em>"Bob didn't step forward, which means Bob must see at least one other muddy child. Since I see no other muddy child besides Bob, I must be the second muddy child!"</em></li> <li data-xf-list-type="ul">Bob goes through the exact same deduction.</li> <li data-xf-list-type="ul">On the second request, <strong>both Alice and Bob step forward simultaneously</strong>. </li> </ul></li> </ul></li> </ol></blockquote><p></p>
[QUOTE="Hawkman, post: 445097, member: 23715"] How the Logic Works (Example with k = 2 Muddy Children: Alice and Bob) [LIST=1] [*][LIST] [*][B]Round 1:[/B] [LIST] [*]Alice sees that Bob is muddy. She thinks: [I]"If I am clean, then Bob is the only muddy child. Bob sees no other muddy children, so Bob should realize he is muddy and step forward immediately."[/I] [*]Bob looks at Alice and thinks the exact same thing. [*]When the parent asks the first time, [B]neither Alice nor Bob steps forward[/B], because each is waiting to see if the other moves. [/LIST] [/LIST] [LIST] [*][B]Round 2:[/B] [LIST] [*]Alice sees Bob [I]didn't[/I] step forward on Round 1. She reasons: [I]"Bob didn't step forward, which means Bob must see at least one other muddy child. Since I see no other muddy child besides Bob, I must be the second muddy child!"[/I] [*]Bob goes through the exact same deduction. [*]On the second request, [B]both Alice and Bob step forward simultaneously[/B]. [/LIST] [/LIST] [/LIST] [/QUOTE]
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