Question 626002: Using the digits 8,3,2,9,0,4 and 6 find the sum of the greatest possible 7 digit odd number and the least possible 7 digit odd number
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
To make the largest number the largest possible digits must be as far
to the left as is possible.
To make the smallest number the smallest possible digits must be as far
to the left as is possible.
We make 7 blanks to fill in with digits:
_ _ _ _ _ _ _
To get the largest odd 7-digit number choose the largest possible of
8,3,2,9,0,4 and 6
which is 9. So the number so far is
9 _ _ _ _ _ _
That leaves 8,3,2,0,4 and 6
Since the digit must be odd, it must end in an odd digit,
and the only odd digit left is 3. So the number so far is
9 _ _ _ _ _ 3
That leaves 8,2,0,4 and 6
Choose the largest for the 2nd digit, which is 8.
So the number so far is
9 8 _ _ _ _ 3
That leaves 2,0,4 and 6
Choose the largest for the 3rd digit, which is 6.
So the number so far is
9 8 6 _ _ _ 3
That leaves 2,0, and 4
Choose the largest for the 4th digit, which is 4.
So the number so far is
9 8 6 4 _ _ 3
That leaves 2 and 0
Choose the larger for the 5th digit, which is 2.
So the number so far is
9 8 6 4 2 _ 3
The only one left is 0, so it goes 6th, and the largest
odd 7-digit number that can be made with those digits is
That leaves 2,0, and 4
Choose the largest for the 4th digit, which is 4.
So the number so far is
9 8 6 4 2 0 3
------------------------------------------------------
_ _ _ _ _ _ _
To get the smallest odd 7-digit number we would like to choose
the smallest possible digit of
8,3,2,9,0,4 and 6
which is 0. However we cannot choose 0 for it must be a 7-digit
number, and it cannot start with 0, so we must choose the next
smallest,
which is 2. So the number so far is
2 _ _ _ _ _ _
That leaves 8,3,9,0,4 and 6
Choose the smallest for the 2nd digit, which is 0.
So the number so far is
2 0 _ _ _ _ _
That leaves 8,3,9,4 and 6
Choose the smallest for the 3rd digit, which is 3.
So the number so far is
2 0 3 _ _ _ _
That leaves 8,9,4 and 6
Choose the smallest for the 4th digit, which is 4.
So the number so far is
2 0 3 4 _ _ _
That leaves 8,9 and 6
Choose the smallest for the 5th digit, which is 6.
So the number so far is
2 0 3 4 6 _ _
That leaves 8 and 9
Choose the smallest for the 5th digit, which is 8.
(We must save the 9 till last anyway to make the number odd)
So the number so far is
2 0 3 4 6 8 _
The only one left is the 9, so it goes 6th, and the smallest
odd 7-digit number that can be made with those digits is
2 0 3 4 6 8 9
Answer: 9864203 + 2034689 = 11898892
Edwin
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