@Ryan: Got it! I like your method -- just keep eliminating square numbers until you're left with what you need.
I still wanted to figure out why my original method was wrong. And it finally dawned on me:
My mistake was not realizing that my answer of 241 was just a lower bound. The value of n needed to be AT LEAST 241, because my analysis said that 241 needed to be divided out. But any number >241 would also do the job of dividing out 241. So I needed to think about higher numbers too.
I still wanted to figure out why my original method was wrong. And it finally dawned on me:
My mistake was not realizing that my answer of 241 was just a lower bound. The value of n needed to be AT LEAST 241, because my analysis said that 241 needed to be divided out. But any number >241 would also do the job of dividing out 241. So I needed to think about higher numbers too.
on /blog/107