Explain the solution:
I noticed that for the three consecutive digits in the four digit number had to be 4,5, and 6 because if it was 0,1, and 2, it would not be able to make a 5 digit number when multiplied by 3, and when it was anything above 4,5, and 6 the third digit (the sum of 2 of consecutive numbers) would be a two digit number which is not possible so the only one possible is 4,5, and 6 because the third digit would be 9 as 4+5=9.
After that the last digit would not be able to be 5 because 5 X 3 = 15 which would repeat 5. 6 would not be in the last digit either because 3 X 6 would repeat 8 which cannot happen. So the only possible one for the last digit is 4.
Thirdly, the second digit could not be 5 because 6 X 3 =18 which then would result in repeating 6, so the only possible one would be 6.
Since 5 is the only one left the top number would be 5694 and since 5694 X 3 = 17084 and 17084 does not repeat, it is the correct answer.