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

Image Credit: Dreamstime
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