In the numbers from 1 to 8000, how many pieces of 1 are used altogether?
Answer
3400 pieces
Solution
(1) The number of pieces which 1 is used for the one's place
3400 pieces
Solution
(1) The number of pieces which 1 is used for the one's place
It's from 0001 to 7991.
When this number is shown as ABC1, the number which applies to A is 8 pieces from 0 to 7.
The number which applies to B is 10 pieces from 0 to 9.
The number which applies to C is 10 pieces from 0 to 9.
Thus there are 8 × 10 × 10 = 800 pieces altogether.
(2) The number which 1 is used for the ten's place
It can be thought by the same way as (1).
The number which applies to D in DE1F is 8 pieces from 0 to 7.
The number which applies to E is 10 pieces from 0 to 9.
The number which applies to F is 10 pieces from 0 to 9.
Thus there are 8 × 10 × 10 = 800 pieces altogether.
(3) The number which 1 is used for the hundred's place
There are also 8 × 10 × 10 = 800 pieces.
(4) The number by which 1 is used for the thousand's place
The number which applies to X in 1XYZ is 10 pieces from 0 to 9.
The number which applies to Y is 10 pieces from 0 to 9.
The number which applies to Z is 10 pieces from 0 to 9.
Thus there are 10 × 10 × 10 = 1000 pieces altogether.
Therefore there are 800 × 3 + 1000 = 3400 pieces.
