The other tutor is all wrong. He doesn't even understand what you're
to do. Here's the explanation:
arrange the digits 0 to 9 into two five-digits numbers who sum is
What we need to realize here is that the digits farther to the left
contribute the most toward the sum and the digits farther to the right
contribute the least toward the sum.
a.The least possible sum of any arrangment
We start with these blanks to fill in with digits
_ _ _ _ _
+ _ _ _ _ _
_ _ _ _ _
The left-most digits contribute the most to the sum, so to make them contribute
the least to the sum, choose the smallest ones to go leftmost. The smallest
possible first digits are 1 nd 2. (Can't use 0 for a first digit!). It doesn't
matter whether the 1 is the first digit of the first number and the 2 is the
first digit of the second digit, or vice-versa I'll do it this way:
1 _ _ _ _
+ 2 _ _ _ _
_ _ _ _ _
The digits farthest to the left contribute the most to the sum, so to make
them contribute the least, choose the two smallest possible remaining digits to
go leftmost. The smallest remaining digits are 0 and 3 It doesn't matter
whether the 0 is the first digit of the first number and the 3 is the first
digit of the second digit, or vice-versa. I'll do it this way:
1 0 _ _ _
+ 2 3 _ _ _
_ _ _ _ _
The next smallest two of the remaining digits are 4 and 5, so they go next:
1 0 4 _ _
+ 2 3 5 _ _
_ _ _ _ _
The next smallest two of the remaining digits are 6 and 7, so they go next:
1 0 4 6 _
+ 2 3 5 7 _
_ _ _ _ _
Finally the only remaining digits are the largest two 8 and 9, so they go last,
where they contribute the least amount to the sum:
1 0 4 6 8
+ 2 3 5 7 9
_ _ _ _ _
And now we add to find that smallest sum:
1 0 4 6 8
+ 2 3 5 7 9
3 4 0 4 7
Answer: 34047. You'll get that same sum if you swap any
digit of one number with the corresponding digit of the
other number.
b.The greatest possible sum of any arragment
Since the digits farther to the left contribute the most, we will just
reverse the process for part a, and put the biggest digits first. So we
put 9 and 8 first. We just always use the biggest two remaining digits
instead of the smallest ones, and we get this:
9 7 5 3 1
+ 8 6 4 2 0
1 8 3 9 5 1
Answer: 183951
Edwin
