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'Double with 1 to 9' printed from https://nrich.maths.org/
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