Henry Ernest Dudeney/Modern Puzzles/57 - A Misunderstanding

by : $57$

 * A Misunderstanding
 * An American correspondent asks me to find a number composed of any number of digits that may be correctly divided by $2$
 * by simply transferring the last figure to the beginning.


 * He has apparently come across our last puzzle with the conditions wrongly stated.


 * If you are to transfer the first figure to the end it is solved by $315 \, 789 \, 473 \, 684 \, 210 \, 526$,
 * and a solution may easily be found from this with any given figure at the beginning.


 * But if the figure is to be moved from the end to the beginning, there is no possible solution for the divisor $2$.


 * But there is a solution for the divisor $3$.


 * Can you find it?