Question 973144: Can we add three odd numbers and to get thirty
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The  th odd number is  , The  th odd number is  . The sum:
\ +\ (2m\ -\ 1)\ =\ 2n\ +\ 2m\ -\ 2)
Since each term of the sum is divisible by 2, the sum is even. Hence, the sum of any two odd numbers is even.
The th even number is  , The th odd number is . The sum:
\ +\ (2m\ -\ 1)\ =\ 2n\ +\ 2m\ -\ 1)
This sum is odd, hence the sum of any even number and any odd number is odd.
So, can three odd numbers total 30? The first two odd numbers you choose will sum to an even number. Then the third odd number, added to the even sum of the first two, will, perforce, be odd. But 30 is even.
John
My calculator said it, I believe it, that settles it
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