As for the integer of three digit that the sum becomes 10 when add the number of hundreds digit, the number of tens digit and the number of ones digit like 235 and 307, answer the following questions.
(1) In such integers, find the number of integer that hundreds digit is 1.
(2) In such integers, find the number of integer that hundreds digit is 5.
(3) Find the all the number of such an integer.
(4) In such integers, find the number of integer that tens digit is 1.
(5) Find the total sum of such an integer.
Answer
(1) Ten
(2) Six
(3) 54
(4) Nine
(5) 22815
Solution
(1) As for the number in the hundreds digit of is 1 and qualifying the conditions, the sum of the numbers in tens digit and ones digit becomes 9.
In this case , there are ten ways of 0 ~ 9 numbers in tens digit.
Therefore number of integer is ten.
(2) As for the number in the hundreds digit of is 5 and qualifying the conditions, the sum of the numbers in tens digit and ones digit becomes 5.
In this case , there are six ways of 0 ~ 5 numbers in tens digit.
Therefore number of integer is six.
(3) If the number of hundreds digit and tens digit are fixed, the number in ones digit is automatically fixed.
The number of all is found by compiling and organizing hundreds and tens digit in a chart.
It is 54 pieces in total as follows.
(4) As for the number in the tens digit of is 1 and qualifying the conditions, the sum of the numbers in hundreds digit and ones digit becomes 9.
In this case , there are nine ways of 1 ~ 9 numbers in hundreds digit.
Therefore number of integer is nine.
(5) Compiling and organizing including ones digit in a chart as follows,
the sum total of the number of hundreds digit is
1 × 10 + 2 × 9 + 3 × 8 + 4 × 7 + 5 × 6 + 6 × 5 + 7 × 4 + 8 × 3 + 9 × 2 = 2100
the sum total of the number of tens digit is
1 × 9 + 2 × 8 + 3 × 7 + 4 × 6 + 5 × 5 + 6 × 4 + 7 × 3 + 8 × 2 + 9 × 1 =165
the sum total of the number of ones digit is same as above.
Therefore, the sum of all the integers, 100 × 210 + 10 × 165 + 1 × 165 = 22815.
(1) In such integers, find the number of integer that hundreds digit is 1.
(2) In such integers, find the number of integer that hundreds digit is 5.
(3) Find the all the number of such an integer.
(4) In such integers, find the number of integer that tens digit is 1.
(5) Find the total sum of such an integer.
(1) Ten
(2) Six
(3) 54
(4) Nine
(5) 22815
Solution
(1) As for the number in the hundreds digit of is 1 and qualifying the conditions, the sum of the numbers in tens digit and ones digit becomes 9.
In this case , there are ten ways of 0 ~ 9 numbers in tens digit.
Therefore number of integer is ten.
(2) As for the number in the hundreds digit of is 5 and qualifying the conditions, the sum of the numbers in tens digit and ones digit becomes 5.
In this case , there are six ways of 0 ~ 5 numbers in tens digit.
Therefore number of integer is six.
(3) If the number of hundreds digit and tens digit are fixed, the number in ones digit is automatically fixed.
The number of all is found by compiling and organizing hundreds and tens digit in a chart.
It is 54 pieces in total as follows.
(4) As for the number in the tens digit of is 1 and qualifying the conditions, the sum of the numbers in hundreds digit and ones digit becomes 9.
In this case , there are nine ways of 1 ~ 9 numbers in hundreds digit.
Therefore number of integer is nine.
(5) Compiling and organizing including ones digit in a chart as follows,
the sum total of the number of hundreds digit is
1 × 10 + 2 × 9 + 3 × 8 + 4 × 7 + 5 × 6 + 6 × 5 + 7 × 4 + 8 × 3 + 9 × 2 = 2100
the sum total of the number of tens digit is
1 × 9 + 2 × 8 + 3 × 7 + 4 × 6 + 5 × 5 + 6 × 4 + 7 × 3 + 8 × 2 + 9 × 1 =165
the sum total of the number of ones digit is same as above.
Therefore, the sum of all the integers, 100 × 210 + 10 × 165 + 1 × 165 = 22815.
