We can rotate in the reverse direction : 142857 × 5 = 714285, the last digit has become the first.

Such a number (142857) is a "Derviche number", rotating by multiplication.

Even more, when multiplying by 2,3,4,5,6, we get all its circular shifts.

Excluding such excess, just find the smallest number, which multiplied by 2 rotates one digit right

Solution

Rotate one digit left ?

Solution

Same questions when multiplying by 3, 4, ... 9

Solution