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If you've got a group of 20 to 30, a fun "audience participation" talk for a picnic could be given on the Josephus problem (participants are put in a circle and every other one is eliminated until a single one remains), perhaps presented as "Survivor: Math Island." Have the students form a circle, hand one of them a token "sword" to start things off, and then insert yourself cleverly in the crowd so as to be the sole survivor. You can have the group next split into subgroups to experiment with different starting numbers and let them discover the power-of-two basis behind the survivorship algorithm, and you can wrap things up by talking about what's known and not known for variants where you knock out every third or fourth person going around the circle, instead of every second.

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If you've got a group of 20 to 30, a fun "audience participation" talk for a picnic could be given on the Josephus problem, perhaps presented as "Survivor: Math Island." Have the students form a circle, hand one of them a token "sword" to start things off, and then insert yourself cleverly in the crowd so as to be the sole survivor. You can have the group next split into subgroups to experiment with different starting numbers and let them discover the power-of-two basis behind the survivorship algorithm, and you can wrap things up by talking about what's known and not known for variants where you knock out every third or fourth person going around the circle, instead of every second.