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Digit Replacement and Square Settlement (Posted on 2022-04-11) Difficulty: 3 of 5
Consider a perfect square N having 1 as the first digit (reading from left).
Determine the minimum value of N such that it remains a perfect square when 1 is replaced by 2.
Find, if possible, the next higher value of N less than 1010 with this property.
Otherwise, prove its non-existence.
Note: Computer-program based methodology apart from semi-analytic solution is permissible.

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

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No SubjectK Sengupta2022-08-02 10:07:43
Hints/TipsGoing much furtherBrian Smith2022-04-11 12:19:25
SolutionAnalytic SolutionBrian Smith2022-04-11 12:11:31
Solutiongoing fartherCharlie2022-04-11 08:17:18
SolutionSolutionJer2022-04-11 07:39:00
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