Steps
1. Units of 5 digit number can't be 0 or 5 because they don't appear in the 3 times table if you use each number once and can't go up to 10 x 3
2. The first digit of the 5 digit number can only be 1 or 2 because otherwise it would be too large to be the answer to 3 x a 4 digit number
3. Therefore the consecutive numbers used at the bottom are 0, 1, 2 (the three is already used)
4. The three consecutive numbers used in the four digit number are 4, 5, 6. So that two of them sum to a single digit number (4 + 5 = 9).
the 10s digit of the 4 digit number is therefore 9.
5. We know where the 9 is. 3 x 9 = 27. The 10s. digit of the 5 digit would be a 7 or 8 (if a 1 is carried over). However we now know that a 2 is carried over to the 100s column.
Three options are available (we already know the number at the bottom has to be a 0, 1, 2.
4 x 3 = 12 (add the carried over 2) 14 - not a possible solution
5 x 3 = 15 (add the carried over 2) 17 - not a possible solution
6 x 3 = 18 (add the carried over 2) 20 - correct solution
Therefore the 100s digit of the 4 digit number is a 6
6. Units digit of the 4 digit number is either a 4 or 5 (we've used the 6). The unit at the bottom is either a 0, 1, 2. Therefore it has to be 4.
7. Place the remaining 5 and 7 so the multiplication is correct
5 6 9 4
x 3
1 7 0 8 2