Question 1024875
The number that is multiplied by itself can't be a 
1-digit number. It can't be a 3-digit number, so
it must be a 2-digit number.
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Also, the units digit must be odd since
( odd )x( odd) = odd in order to make {{{ c }}} odd
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It can't be as large as {{{ 33 }}}, since {{{ 33^2 = 1089 }}}
I could be as large as {{{ 31 }}}, since  {{{ 31^2 = 961 }}}
It could be as small as {{{ 11 }}}, since {{{ 11^2 = 121 }}}
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So, the possible numbers and their squares are:
11 - 121
13 - 169
15 - 225
17 - 289
19 - 361
21 - 441
23 - 529
25 - 625
27 - 729
29 - 841
31 - 961
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The sum of the digits of {{{ 13^2 = 169 }}} is {{{ 16 }}}
The sum of the digits of {{{ 23^2 = 529 }}} is {{{ 16 }}}
The sum of the digits of {{{ 31^2 = 961 }}} is {{{ 16 }}}
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I think the number can be
169, 529, or 961