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