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...

Seven from Nine

Age 11 to 14 ShortChallenge Level

Choosing 7 numbers is the same as choosing which 2 numbers to leave out
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
= (1 + 9) + (2 + 8) + (3 + 7) + (4 + 6) + 5 = 45

45 is a multiple of 3
$\therefore$ the two left out add up to a multiple of 3

3,6   3,9   6,9   are the ways of pairing two multiples of 3

1,2   1,5   1,8   are the ways of pairing 1 with a number 1 less than a multiple of 3

4,2   4,5   4,8
7,2   7,5   7,8   are the ways of pairing the other numbers which are 1 more than
a multiple of 3 with a number 1 less than a multiple of 3

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