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Several solutions.

17 + 1 + 1 + 1 + 1

15 + 3 + 1 + 1 + 1

13 + 5 + 1 + 1 + 1, 13 + 3 + 3 + 1 + 1

11 + 7 + 1 + 1 + 1, 11 + 5 + 3 + 1 + 1, 11 + 3 + 3 + 3 + 1

9 + 9 + 1 + 1 + 1, 9 + 7 + 3 + 1 + 1, 9 + 5 + 5 + 1 + 1, 9 + 5 + 3 + 3 + 1

7 + 7 + 5 + 1 + 1, 7 + 7 + 3 + 3 + 1, 7 + 5 + 5 + 3 + 1, 7 + 5 + 3 + 3 + 3

5 + 5 + 5 + 5 + 1

Note that there is only one solution that does not include 1, namely 7 + 5 + 3 + 3 + 3

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Q: What five odd numbers add up to twenty-one?
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What five odd numbers equal 100?

This has no answer. Any five odd numbers will always add to an odd number. 100 is even.


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You can't find five odd numbers that add up to fifty; the sum of five odd numbers will always be odd.


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