### 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 ShortChallenge 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 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

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.