Question

We call a number special if every digit in the number either is a 1 or borders a 1. For example, 11111, 13, 141, 1441, 515151, and 101 are all special, but 10001, 222, 122, and 1333 are not special.

How many 3-digit numbers are special?

Answer 1

I do not understand the definition, repeat and be clear.

Answer 2

Never mind, I get it.

Answer 3

ok
we divide the solution to 3 parts

1. special 3-digit numbers with 3 one in their digits
we have one 3-digit numbers with this property : 111 1 answer from here

2. special 3-digit numbers with 2 one in their digits
11a or 1a1 or a11
for 11a a={0,2,3,4,5,6,7,8,9} 9 answers from here
for 1a1 a={0,2,3,4,5,6,7,8,9} 9 answers from here
for a11 a={2,3,4,5,6,7,8,9} 8 answers from here

3. special 3-digit numbers with 1 one in their digits
the 1 must be in the midlle like ----> a1b
a={2,3,4,5,6,7,8,9}
b={0,2,3,4,5,6,7,8,9}
answers from here 9*8=72

so u have 1+9+9+8+72=99 special 3-digit numbers