Question 1096948: What's the sum of all the three-digits numbers I can form from digits 0-9 if
REPITITION is PROHIBITED
Found 3 solutions by jorel1380, Edwin McCravy, KMST:
Answer by jorel1380(3719)   (Show Source):
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! The above is incorrect. Sorry, Jorrell.
If the hundreds digits could be 0's, the problem would be much
easier. So let's begin by pretending that the hundreds digits
can be 0, and finding that sum first. Then we will find the
sum of those with 0's as the hundreds digit, and subtract.
Suppose we had them all listed to add like this:
012
013
014
...
...
098
102
103
...
...
...
986
+987
----
sum
There are 10*9*8 = 720 numbers in that list. There are an
equal number of each digit in each column, so there are 720/10
or 72 of each digit in each column. Since the sum of the digits
0+1+2+3+4+5+6+7+8+9 = 45, the sum of each of the three columns
of digits is 45*72 = 3240.
The hundreds column will contribute 324000 toward the sum, the
tens column will contribute 32400, and the ones column will
contribute 3240, so the sum is 324000+32400+3240 = 359640. That
would be the answer if 0 could be used as the hundreds digit of
a 3 digit number. But alas, it cannot! :)
So now we calculate how much we must subtract from the 359640.
We must now find the sum of this list:
012
013
014
...
...
098
----
Since the hundreds digits are all 0's there are no 0's in the
tens or ones digit columns. So there are 9*8 = 72 numbers in
that list. There are an equal number of each digit, 1 though
9 in each of the tens and ones columns, so there are 72/9 or
8 of each digit 1 thru 9 in the tens and ones columns. Since
the sum of the 9 digits 1+2+3+4+5+6+7+8+9 = 45,
the sum of each of the two columns of digits is 45*8 = 360.
The tens column will contribute 3600 toward the sum, and the
ones column will contribute 360, so the sum is 3600+360 = 3960.
So we subtract that from 359640.
Answer = 359640-3960 = 355680
Edwin
Answer by KMST(5328)  (Show Source):
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