You may also like

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Calendar Capers

Choose any three by three square of dates on a calendar page...

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Double with 1 to 9

Age 11 to 14 Short
Challenge Level

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               8     3, 5, 7, 9 left                    1               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     5               2, 4, 9 left                        1     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


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.