SOLUTION: compute how many four-digit integers use each of the digits 3,4,7,8 once and are divisible by 11 compute the sum of the digits of the integers from 350 to 400, inclusive

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Question 227880: compute how many four-digit integers use each of the digits 3,4,7,8 once and are divisible by 11

compute the sum of the digits of the integers from 350 to 400, inclusive
Answer by Alan3354(21583) About Me  (Show Source):
You can put this solution on YOUR website!
compute how many four-digit integers use each of the digits 3,4,7,8 once and are divisible by 11
3784 = 11*344
3487 = 11*317
4378 = 11*398
4873 = 11*443
7348 = 11*668
7843 = 11*713

compute the sum of the digits of the integers from 350 to 400, inclusive
51 numbers. The average = (350+400)/2 = 375
51*375 = 19125
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If you mean the sum of individual digits:
In the 100s position there are:
50 3's and 1 4 = 154
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In the 10s position there are:
10 5's, 10 6's, 7's, 8's and 9's
--> 50 digits with average of 7 = 350
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In the 1's there are:
0-9 5 times
= 5*9*avg(1-9) = 5*9*5 = 225
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154+350+225 = 729
729 = 3^6, but I don't see any connection