### Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# Football Champs

##### Stage: 3 Challenge Level:

Three teams A, B and C have each played two matches. Three points are given for a win and one point to each team for a draw. Here are the results given by Lim Zi Heng, Goh Wei Ming, Chong Ching Tong, Chan Hei Leong, Chen Wei Jian and Ng Yan Shun from River Valley High School, Singapore, Kenneth Macleod, Forres Academy and Daniel Pick, Bourne Grammar School.

Teams Games
Played
Won Drawn Lost Goals
for
Goals
against
Points
A 2 1 0 1 5 3 3
B 2 0 1 1 2 5 1
C 2 1 1 0 3 2 4

The scores are A versus B = 4-1, B versus C = 1-1 and C versus A= 2-1. Kenneth explained how, given the information in the table below, he got all the results (being football mad he said).

Teams Games
Played
Won Drawn Lost Goals
for
Goals
against
Points
A 2       5 3 3
B 2       2   1
C 2       3 2 4

Team A have obviously won 1 game and lost 1 game because they have three points which means they have won 1 game and because all the teams have played 2 games, they have lost a game too. If team A had drawn a game they would have 4 points. So team A beat team B(4-1) and lost to team C(1-2).

With 3 matches there are few possibilities. With more teams and more matches you can use algebra to find the missing information.

In future months we'll publish problems of this sort created and sent in by members. Can you create one? You can have more teams and more matches.