Consider a perfect square having 3 as the first digit (reading left to right).
Determine the minimum value of N such that N remains a perfect square when the first digit is changed to 5.
sqs=(1:60000000).^2;
sqs=sqs(floor(sqs./10.^floor(log10(sqs)))==3);
for i=1:length(sqs)
v=sqs(i);
sq=num2str(v);
sq(1)='5';
sq=str2double(sq);
sr=round(sqrt(sq));
if sr*sr==sq
fprintf('%17d %10d %17d %10d \n',[v sqrt(v) sq sr])
end
end
finds the first such N is 30625:
N sqrt(N) replacement sqrt(replacement)
30625 175 50625 225
3062500 1750 5062500 2250
306250000 17500 506250000 22500
30625000000 175000 50625000000 225000
315703515625 561875 515703515625 718125
3062500000000 1750000 5062500000000 2250000
31570351562500 5618750 51570351562500 7181250
306250000000000 17500000 506250000000000 22500000
3157035156250000 56187500 5157035156250000 71812500
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Posted by Charlie
on 2025-03-31 10:45:32 |
computer solution
