# Calvin and Susan play a Number-Game #2

Logic Level 5

Calvin writes a number with 2187 digits on the blackboard, each digit being either a 1 or 2. Susan creates a new number from Calvin's number by reading his number from left to right and wherever she sees a 1, replacing that by 112, and wherever she sees a 2, replacing that by 111.

For example : If Calvin's number begins $$2112$$, Susan's number would begin $$111112112111$$.

After Susan finishes writing her number, she notices that the left-most 2187 digits in her number is exactly same as that of Calvin's number. How many times do five $$1$$s occur consecutively in Calvin's number?

Also try it's sister problem, an easy version: Calvin and Susan play a Number-Game #1

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