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BEBRAS 2021 Grade 9-10 Round 2 Ext Question 12

BEBRAS · BEBRAS 2021 Grade 9-10 Round 2 Ext

Question 12

Alex has a wooden box with nine compartments and nine balls. He may choose how many balls to use. Every ball must lie in one compartment, each compartment holds at most one ball, and the number of balls in every row and every column must be odd.

Question illustration

How many different arrangements satisfy all conditions?
  1. 12
  2. 16
  3. 64
  4. 120