Integers greater than 1000 are created using the digits 2, 0, 1, 4 exactly once in each integer.
What is the difference between the average of the largest and smallest of these integers that can be created this way?
largest : 4210
smallest: 1024
average = (4210+1024)/2 = ...
2617
To find the average of the largest and smallest integers that can be created using the digits 2, 0, 1, 4 exactly once in each integer greater than 1000, we need to find the largest possible integer and the smallest possible integer that can be formed.
To find the largest possible integer, we arrange the digits in descending order. So, the largest integer will start with the digit 4, followed by 2, then 1, and finally 0. The largest possible integer formed using these digits is 4210.
To find the smallest possible integer, we arrange the digits in ascending order. So, the smallest integer will start with the digit 0, followed by 1, then 2, and finally 4. The smallest possible integer formed using these digits is 0124.
Now, we can calculate the difference between the largest and smallest integers:
Largest Integer: 4210
Smallest Integer: 0124
The difference = Largest Integer - Smallest Integer = 4210 - 0124
To subtract these numbers, we need to make sure they have the same number of digits by adding leading zeros to the smaller number:
4210 - 0124 = 4210 - 0124 = 4210 - 124
Now, subtracting the numbers:
4210 - 124 = 4086
So, the difference between the average of the largest and smallest integers that can be created using the digits 2, 0, 1, 4 exactly once in each integer greater than 1000 is 4086.