(1) There are 2 digits of numbers of 10, 11, 12, 13, .... 99.
Multiple each tens digit and ones digit number of each number and make 90 pieces of numbers.
Find the sum total of 90 numbers.
(2) There are 4 digits of numbers of 1000, 1001, 1002, 1003, .... 2013.
Multiple each of thousands, hundreds, tens and ones digit number of each number and make 1014 pieces of numbers.
Find the sum total of 1014 numbers.
(3) Among 2014 pieces of numbers made in (2), find the pieces of figures whose ones digit is 7.
Answer
(1) 2025
(2) 91125
(3) 16 pieces
Solution
（1）As for 10, 11, 12, 13,......,19, 1×0+1×1+1×2+1×3+....+1×9 = 45.
As for 20，21，22，23・・・・・，29， 2×（1 + 2 + 3 +……+ 9）＝2×45.
As for 30，31，32，33，・・・・・39，3×45.
As for 90，91，92，93・・・・・，99，9×45.
Thus sum total is 45 + 2×45 ＋ 3×45＋・・・・・＋9×45＝（1+2+3+・・・・・+9）×45＝45×45=2025.
(2) As for 10XX, total is zero.
Multiple each tens digit and ones digit number of each number and make 90 pieces of numbers.
Find the sum total of 90 numbers.
(2) There are 4 digits of numbers of 1000, 1001, 1002, 1003, .... 2013.
Multiple each of thousands, hundreds, tens and ones digit number of each number and make 1014 pieces of numbers.
Find the sum total of 1014 numbers.
(3) Among 2014 pieces of numbers made in (2), find the pieces of figures whose ones digit is 7.
Answer
(1) 2025
(2) 91125
(3) 16 pieces
Solution
（1）As for 10, 11, 12, 13,......,19, 1×0+1×1+1×2+1×3+....+1×9 = 45.
As for 20，21，22，23・・・・・，29， 2×（1 + 2 + 3 +……+ 9）＝2×45.
As for 30，31，32，33，・・・・・39，3×45.
As for 90，91，92，93・・・・・，99，9×45.
Thus sum total is 45 + 2×45 ＋ 3×45＋・・・・・＋9×45＝（1+2+3+・・・・・+9）×45＝45×45=2025.
(2) As for 10XX, total is zero.
As for 11XX, total is 2025 which is the same as (1).
As for 12XX，2 × 2025.
As for 13XX，3×2025.
・・・・・・・
As for 19XX，9×2025.
As for 2000～2013, total is zero.
Thus the sum total is (1 + 2 + 3 + ・・・・・ + 9）× 2025＝45 × 2025 ＝ 91125.
(3) As for 1XXX, examine the combination of three numbers of hundreds digit, tens digit and ones digit whose product is to be 7.
Combination （1，1，7）・・・3 ways
（1，3，9）・・・6 ways
（3，3，3）・・・1 way
（3，7，7）・・・3 ways
（7，9，9）・・・3 ways
Therefore sum total is 3 + 6 + 1 +3 + 3 = 16 pieces.
As for 12XX，2 × 2025.
As for 13XX，3×2025.
・・・・・・・
As for 19XX，9×2025.
As for 2000～2013, total is zero.
Thus the sum total is (1 + 2 + 3 + ・・・・・ + 9）× 2025＝45 × 2025 ＝ 91125.
(3) As for 1XXX, examine the combination of three numbers of hundreds digit, tens digit and ones digit whose product is to be 7.
Combination （1，1，7）・・・3 ways
（1，3，9）・・・6 ways
（3，3，3）・・・1 way
（3，7，7）・・・3 ways
（7，9，9）・・・3 ways
Therefore sum total is 3 + 6 + 1 +3 + 3 = 16 pieces.
