Can you find a number which added to itself one or several times will give a total having the same digits as that number but differently arranged and after the sixth addition will give a total of all nines?
Answer
142857.
The number and the sums will only contain the digits 1,2,4,5,7 and 8.
142857 + 142857 = 285714
142857 + 142857 + 142857 = 428571
142857 + 142857 + 142857 + 142857 = 571428
142857 + 142857 + 142857 + 142857 + 142857 = 714285
142857 + 142857 + 142857 + 142857 + 142857 + 142857 = 857142
142857 + 142857 + 142857 + 142857 + 142857 + 142857 + 142857 = 999999