** Posted On** 2016-10-04

** Answer** 1) 3 digit numbers that can be formed with repetition of digits using 1,2,3,4 is 4×4×4= 64. This is because 1st digit can be any one out of 4 available digits. Similarly we can say for 2nd and 3rd digit.
2) Out of these 64 numbers, 16 numbers will begin with 1, 16 will begin with 2, 16 will begin with 3 & 16 will begin with 4. This is because every digit has an equal occurence.
3) Hence, for the first digit 1,2,3,4 has to be added each 16 times. This is same as 16×(1+2+3+4)= 160. Similarly we can say sum of digits for tens place and units place will be 160.
4) To arrive at sum of all the 3 digit numbers we have to add all the sums obtained in step 3 (Don't forget the place value for the sum of the digits). Hence the required sum is 160×100+ 160×10+ 160= 160(100+10+1)= 160×111= 1776

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