Show that the numbers of the form:
444444....4444888888....8889
[Where there are 'k' Fours, '(k-1)' Eights and 'Exactly One' 9],
are always perfect squares.
(For example the sequence of numbers: 49, 4489, 444889, ....etc. and so on are always perfect squares).
(In reply to
solution by Charlie)
Suppose the digits from 0 through 9 occurred in random order in the square roots of the numbers of the given sequence, instead of following a definite pattern like 7, 67, 667, 6667,....,etc., then how would you have proceeded to solve the given problem ? I need that kind of a proof Charlie.
Anyway, I am not saying that your method is wrong. it is absolutely correct and nice one too but all I want is a different approach and a shorter method. That's it. :)
re: solution
