What is the smallest k-digit number so that its last pair of digits is k times the first pair of digits?
(In reply to re(3): Possible solution
by Ady TZIDON)
'It' will work for most k, but not any k.
The definition of a pair being implied is two things of the same type, thus the mininum number of digits must be two.
As to the whether 00 is a 2-digit number (or 0000000000000 as a 13-digit number), it is. What it is not is the standard or simplest representation of the number.
Standard and simplest representation aside, and excluding leading zeroes, yet by stipulating that the number is given in a different radix than base-10, a smaller 3-digit number can be represented. In base-6, 153 has a decimal value of 69. The initial pair, 15, in base-6 has a decimal value of 11, and the last pair, 53, in base-6 has a decimal value of 33, which is 3 times the value of the initial pair.
Posted by Dej Mar
on 2012-06-27 03:36:13