SOLUTION: Find the sum of those numbers between 1000 and 6000 every one of whose digits is one of the numbers 0, 2, 5 or 7. Give your answer as a product of prime numbers.
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Question 580641: Find the sum of those numbers between 1000 and 6000 every one of whose digits is one of the numbers 0, 2, 5 or 7. Give your answer as a product of prime numbers. Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! The first digit cannot be 0 or 7, so the only options are 2 and 5. There will be two sets of numbers, those in the 2000's and those in the 5000's, and there will be the same number with a 2 in the thousands place as with a 5 in the thousands place. The average value of the thousands place digit is 3.5.
There are 4 choices for each of the other 3 digits, making possible combinations, from 000 to 777, and all choices are equally likely so the average value for each digit is .
The total number of 4 digit numbers meeting the requirement is .
The sum of all those numbers is 1000 times the sum of the thousands digits, plus 100 times the sum of the hundreds digits, plus 10 times the sum of the tens digits, plus the sum of the ones digits.
Those sums will be the average for the position (3.5 for all positions) times the number of digits in that position added (128 in each case).
So the sum of all 128 numbers is
