Double with 1 to 9

Answer: There are 12 possible pairs:
6729 & 13458
6792 & 13584
6927 & 13854
7269 & 14538
7293 & 14586
7329 & 14658
7692 & 15384
7923 & 15846
7932 & 15864
9267 & 18534
9273 & 18546
9327 & 18654



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:

6729 & 13458
6792 & 13584
6927 & 13854
7269 & 14538
7293 & 14586
7329 & 14658
7692 & 15384
7923 & 15846
7932 & 15864
9267 & 18534
9273 & 18546
9327 & 18654