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A !* !_ Number Chain !_ !* is created by having a rule that takes any number to some other (not necessarily different) number. Then we start somewhere and see where we end up. For example: * if every number gets doubled, ** every number chain just goes off to infinity. * if every number gets halved (rounding up), ** every number chain ends with 1. * if every number gets halved (rounding down), ** every number chain ends with 0. Now suppose we use the following rule: * If /n/ is even, halve it. * If /n/ is odd, send it to /3n+1/ Questions: * Where does 7 go? * Where does 17 go? * Where does 27 go? * What are the possibilites? * Where does -5 go? It is an unproven conjecture that every positive number eventually ends at 1. ---- See also: Happy Number.