[BB] Find the fault in the following “proof” that in any group of n people, everybody is the same age.
Suppose n = 1. If a group consists of just one person, everybody is the same age. Suppose that in any group of k people, everyone is the same age. Let G − {a1,a2,…, ak+1} be a group of k + 1 people. Since each of the groups {a1, a2,…, ak) and {a2, a3,…, ak+1} consists of k people, everybody in each group has the same age, by the induction hypothesis. Since a2 is in each group, it follows that all k + 1 people a1a2,…, ak+1 have the same age.
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