Pick up three different numbers out of five numbers 1, 2, 3, 4, and 5 and make integers of triple figures.
Find the sum of all the integers made.
Answer
19980
Solution
The number of integers to be made is 5 × 4 × 3 = 60 pieces.
There are 12 numbers whose hundreds digit is 1, 12 numbers whose tens digit is 1 and 12 numbers whose ones digit is 1.
As for each number, it is used 12 times, respectively as the number each of hundreds digit, tens digit and ones digit.
For example, the sum total of 1 is calculated as (1+10+100) × 1 × 12 = 111 × 1 × 12.
The sum total of 2 is calculated as (1+10+100) × 2 × 12 = 111 × 2 × 12.
Therefore, the sum total of all numbers of 1 to 5 is calculated as 111 × (1+2+3+4+5) × 12 = 111 × 15 × 12 = 19980.
<Another solution>
The least number is 123 and the greatest number is 543.
The sum total = (123 + 543) × 60 / 2 = 19980.
Find the sum of all the integers made.
Answer
19980
Solution
The number of integers to be made is 5 × 4 × 3 = 60 pieces.
There are 12 numbers whose hundreds digit is 1, 12 numbers whose tens digit is 1 and 12 numbers whose ones digit is 1.
As for each number, it is used 12 times, respectively as the number each of hundreds digit, tens digit and ones digit.
For example, the sum total of 1 is calculated as (1+10+100) × 1 × 12 = 111 × 1 × 12.
The sum total of 2 is calculated as (1+10+100) × 2 × 12 = 111 × 2 × 12.
Therefore, the sum total of all numbers of 1 to 5 is calculated as 111 × (1+2+3+4+5) × 12 = 111 × 15 × 12 = 19980.
<Another solution>
The least number is 123 and the greatest number is 543.
The sum total = (123 + 543) × 60 / 2 = 19980.
