If you moved the 3 at the end of a certain large number to the beginning, it would be the same as multiplying it by 3. What is the number?
(In reply to
Standard solution by Federico Kereki)
I am fascinated by this nonpractical problem and the method you give. Can you give a reference for the method? Replacing 3 in the problem with 2, I get the 18digit number 105263157894736842. Replacing 3 with n, there will be an answer (perhaps itself containing an internal repeating answer) with 10n2 digits if 10n1 is prime, i.e. when n=2,3,6,8, and 9. When 10n1 is prime, the (10n2)digit answer will be the smallest possible whenever the index of 10 mod 10n1 is coprime to 10n2 as it is for n=2,3, and 6. Thus the minimal answer for n=6 has 58 digits.

Posted by Richard
on 20040302 01:10:08 