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It is not possible for five odd numbers to add up to 50 or any even number. All even numbers have the form 2x, where x is an integer, that is if you divide an even number by two you get an integer. All odd numbers have the form 2x + 1, where x is an integer. Another way of looking at this is that every odd number is an even number plus 1. So lets take five odd numbers, 2v+1, 2w+1, 2x+1, 2y+1, and 2z+1, where v, w, x, y, and z are distinct integers. Adding them together we get: (2v+1) + (2w+1) + (2x+1) + (2y+1) + (2z+1) 2v + 2w + 2x + 2y + 2z + 5 2v + 2w + 2x + 2y + 2z + 4 + 1 2(v + w + x + y + z + 1) +1 This is the form of an odd number. Therefore any five odd numbers added together will sum to an odd number.

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