There are 9 digits altogether so one number will have 4 digits and one will have 5 digits.
The larger number will start with a 1 and the smaller number will start with a number at least 5
The larger number will be even
Try: 6 1 2 3, 4, 5, 7, 8, 9 left
either or 6 4 6 7 1 2 8 3, 5, 7, 9 left 1 2 4
3, 5, 8, 9 left
Stuck! Only odd numbers left but Stuck! 5 doubles to 0 or 1 so cannot
1 has not been carried from ones go on top. But need 7 or 2 on top for
digits! 5 on bottom. Both have been used!
Start again. Try: 6 1 3 2, 4, 5, 7, 8, 9 left
how about: 6 1 3 5 2, 4, 7, 8, 9 left
6 7 1 3 5 2, 4, 8, 9 left
either or 6 7 8 6 7 9 1 3 5 2, 4, 9 left 1 3 5 8 2, 4
left
Stuck! 8 doubles to give 6 or 7 Perfect! 6792 and 13584
There are lots of possibilities.
The table below shows all of the possible starting digits for the four digit and five digit numbers.
smaller number
larger number
6 _ _ _
1 3 _ _ _
7 _ _ _
1 4 _ _ _
7 _ _ _
1 5 _ _ _
8 _ _ _
1 6 _ _ _
8 _ _ _
1 7 _ _ _
9 _ _ _
1 8 _ _ _
Working systematically through each row in the table and finding all of the possible pairs for that row, these are the 12 possible pairs: