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BEBRAS 2017 Grade 5-6 Round 2 Ext Question 13

BEBRAS · BEBRAS 2017 Grade 5-6 Round 2 Ext

Question 13

Replacement rules describe how to rewrite a letter as a string of letters. For example, A→BB and B→ABA replace each A by BB and each B by ABA. Starting with A, these rules give A→BB→ABAABA→BBABABBBBABABB in three steps. At every step, all letters are replaced according to the rules.
Which rule set can produce BAACCACCABAB?

Editorial interpretation: the new target question does not fix an initial letter; it asks whether these rules can produce the target.
  1. A→BAA, B→C, C→BB
  2. A→ACC, B→BA, C→AB
  3. B→BB, A→CC, C→BAB
  4. All three sets above.