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At least one of the numbers must be negative since 1+3+5+7 = 16, which is too big.

Having accepted that, there are infinitely many ways:

1+1+9 + (-1)

1+3+9 + (-3)

and so on

1+5001+9 + (-5001)

and on

and on.

Or with 2 negatives:

1+11 -1 -1

1+13 -1 -3

1+15 -1 -5

1+15 -3 -3

etc

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Q: How many ways can you add four odd numbers to get the sum of 10?
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