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Australian AMC 2017 - Senior Question 22

AMC AUSTRALIA · Australian AMC 2017 - Senior

Question 22

Andy and Brandy have decided to share a cake in an unusual way. Andy will take some fraction of the cake first. From then on, Brandy and Andy will alternate taking half of what remains each time. Eventually there is so little left they decide they are finished. What fraction of the cake should Andy take first to ensure that they end up with half each?
  1. $\frac16$
  2. $\frac14$
  3. $\frac25$
  4. $\frac13$
  5. $\frac12$