Question 939395: SOLUTION: 1 3 5 7
9 11 13 15 17
19=100 , To Make
50 Use Only 5
Digits ...? What
The 5 Digits
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Given:
a set A of 9 odd integers (whole numbers), A={1,3,5,7,9,11,13,15,17}
Objective: obtain a sum of 50 using exactly 5 elements of set A.
Analysis:
Assume it is possible to find 5 numbers n1...n5 such that their sum is 50.
Then
Since all these numbers are odd, each can be represented by n1=2k1+1, where k1 is an arbitrary integer (whole number), and the same for n2...n5.
The sum is then
rearranging,
however, it is evident that 2(k1+k2+k3+k4+k5) is an even number,
therefore
 cannot be a true statement.
Thus we conclude that the initial assumption
is also a false statement.
Conclusion: There is no solution to the given problem, proved by contradiction.
Answer:
There is no solution to this problem because the sum of an odd number of odd numbers is always odd.
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