Question 331009
 If you multiply this odd digit by itself, the sum of the digits of the product is 7. What is the mystery digit? and how.
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It's 5.
If the sum of the digits of the square = 7, the number has to be small.
Try the odd numbers - 1, 3, 5...   5 works.
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49 also works.
149 also works.
1049 also works.
Probably some others.  
Not a well presented problem, it should ask for the smallest odd number that fits.