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BEBRAS 2018 Grade 3-4 Round 2 Ext Question 11

BEBRAS · BEBRAS 2018 Grade 3-4 Round 2 Ext

Question 11

Count binary strings (made only of 0 and 1) with no two adjacent ones, such as 010010001. The table records counts for length N.

Question illustration

For N=1 the strings are 0,1; for N=2 they are 00,01,10; for N=3 they are 000,100,010,001,101. How should the complete count row read?
  1. 2, 3, 5, 7, 9
  2. 2, 3, 5, 10, 15
  3. 2, 3, 5, 8, 13
  4. 2, 3, 5, 8, 14