SOLUTION: SOLUTION: 1 3 5 7 9 11 13 15 17 19=100 , To Make 50 Use Only 5 Digits ...? What The 5 Digits

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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