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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 $3$-digit numbers are memorable?

 Dec 16, 2019
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A 3-digit number is memorable if it is of the form 1B1 or A1C.  This gives us 10 + 10*10 = 110 3-digit memorable numbers.

 Dec 16, 2019

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