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3 Cinnamon Stars

© Friederike Hofmann, MATH+

© Friederike Hofmann, MATH+

Author: Frits Spieksma (TU Eindhoven)
Project: 4TU.AMI

Challenge

On the table, there are an empty red bowl, an empty black bowl, and 16 cinnamon stars. To pass the time, Ruprecht plays a game. In each move, Ruprecht either takes a cinnamon star from the table and puts it into one of the bowls, or he takes a cinnamon star from one of the bowls and puts it back on the table. Ruprecht sticks to the following rules:

  • At the end of every move, the red bowl contains at least as many cinnamon stars as the black bowl.
  • If at the end of a move the red bowl contains exactly R cinnamon stars and the black bowl exactly B cinnamon stars, then Ruprecht is not allowed to have exactly R cinnamon stars in the red bowl and B cinnamon stars in the black bowl at the end of any of the later moves.

 

What is the maximal number M of moves that Ruprecht can perform under these rules?

Possible answers:

  1.  The maximal number is M = 67.
  2.  The maximal number is M = 68.
  3.  The maximal number is M = 69.
  4.  The maximal number is M = 70.
  5.  The maximal number is M = 71.
  6.  The maximal number is M = 72.
  7.  The maximal number is M = 73.
  8.  The maximal number is M = 74.
  9.  The maximal number is M = 75.
  10.  The maximal number is M = 76.
Challenge as PDF