Calvin and Susan play a Number-Game #1

Logic Level 4

Calvin writes a number with 3000 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 122, and wherever she sees a 2, replacing that by 111.

For example : If Calvin's number begins \(2112\), Susan's number would begin \(111122122111\).

After Susan finishes writing her number, she notices that the left-most 2500 digits in her number is exactly same as that of the left-most 2500 digits of Calvin's number. Then find the sum of the seven digits in the positions 2006 to 2012, both inclusive.

Also try it's sister problem, a difficult version: Calvin and Susan play a Number-Game #2

Image Credit: DreamsTime

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