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We call a number memorable if every digit in the number is either a $1$ or adjacent to a $1.$ For example, the numbers $111,$ $81,$ $101,$ and $1771$ are all memorable, but the numbers $12321,$ $786,$ $140,$ and $1999$ are not memorable. How many positive $2$-digit numbers are memorable?

 Dec 21, 2019
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10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91 =18 such numbers.

 Dec 21, 2019

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