I don't know should I ask in Puzzling or not. Sorry for that if I'm wrong! And my question is, I have a lucky number that has four digits which the first three numbers and the last three numbers are perfect square and my lucky number's digits are different. I found the number but I couldn't figure out a mathematical way to solve. Appreciate your help!

  • $\begingroup$ What is the problem? A number as $169324$ is good? $\endgroup$ Dec 13, 2015 at 11:19
  • $\begingroup$ The answer is not unique. (e.g. 289361 and 289576) If you know some program language, you can find possible answers by brute force. $\endgroup$
    – Hanul Jeon
    Dec 13, 2015 at 11:19
  • $\begingroup$ @EmilioNovati I forgot to mention it is four digits $\endgroup$
    – ysn_akst
    Dec 13, 2015 at 11:21
  • $\begingroup$ @HanulJeon I know I got help from Python but I wanted to do with a scientific way. And also look at my edit. The number is 4 digits $\endgroup$
    – ysn_akst
    Dec 13, 2015 at 11:22
  • $\begingroup$ So $4981$ is good? You can test other possible solution by brute force. $\endgroup$ Dec 13, 2015 at 11:22

1 Answer 1


A possible solution is the number $7841$ since : $784=28^2$ and $841=29^2$.

An inspection to a table of squares shows that this is the only possible solution.

  • $\begingroup$ OK, but I really wanted to find a way. Whatever, maybe there is not $\endgroup$
    – ysn_akst
    Dec 13, 2015 at 11:45
  • 1
    $\begingroup$ Not an answer. The OP require that the digits of the number are different. $\endgroup$ Dec 13, 2015 at 13:02

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