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Digit addition and insertion (Posted on 2011-10-27) Difficulty: 2 of 5
(I) Determine all possible base ten 8-digit perfect square(s) N, with no leading zeroes, such that the number obtained by increasing the second digit (reading left to right) of N by 1 is also a perfect square.

(II)Determine all possible base ten 4-digit perfect square(s) N, with no leading zeroes, such that the number obtained by inserting two zeroes between the thousands digit and the hundreds digit of N is also a perfect square.

**** Calculators are allowed, but no computer programs.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution answers | Comment 1 of 2
(I)
24502500 = 49502 :: 25502500 = 50502
38564100 = 62102 :: 39564100 = 62902

(II)
2704 = 522 :: 200704 = 4482
7569 = 872 :: 700569 = 8372

Edited on October 27, 2011, 10:22 pm
  Posted by Dej Mar on 2011-10-27 12:32:53

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