Trivia
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Re: Early Friday Puzzler -- square sums () Alex Y
And you'd think that by the time I reached my age I would have learned to check my work! What could be more basic and easier than to count the items in the list?!
Being more careful, I came up with a list that matches yours (actually the reverse) with your representation of squares. And I still believe that this is the only solution (considering reversing the list to be too trivial to count as a second solution).