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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 21, 2019
 #1
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We can break into cases:

 

111 - 1 number
11* - 10 numbers
1*1 - 10 numbers
*11 - 10 numbers
*1* - 100 numbers

 

This gives us a total of 131 memorable numbers.

 Dec 21, 2019
 #2
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See the answer here:   https://web2.0calc.com/questions/help_27513#r1

 Dec 21, 2019

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