Question

How many 3 digit numbers
are there that get 9 as the
sum of their digits.
Say without writing​

Answer 1

Step-by-step explanation:

Those whose first digit is 1.

Start with the first one 108. This is 9 x 12.

After that it is every ninth number to 180. This is 9 x 20, so we have 20–12+1 = 9.

Those whose first digit is 2.

Start with the first one 207. This is 9 x 23.

After that it is every ninth number to 270. This is 9 x 30, so we have 30–23+1 = 8.

Those whose first digit is 3.

Start with the first one 306. This is 9 x 34

After that it is every ninth number to 360. This is 9 x 40, so we have 40–34+1 = 7.

Are we seeing a pattern here.

Those whose first digit is 4.

Start with the first one 405. This is 9 x 45.

After that it is every ninth number to 450. This is 9 x 50, so we have 50–45+1 = 6.

The pattern is pretty solid.

I am ready to believe there will be 5 whose first digit is 5, 4 whose first digit is 6, 3 whose first digit is 7, 2 whose first digit is 8, and 1 whose first digit is 9.