You may also like

problem icon

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?

problem icon

Clock Squares

Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.

problem icon

Football Champs

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.


Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This solution was submitted by Wymondham High School who reasoned their solution in the following way:

To start off we tried to work out the logical answers. For example where it says 'D had no points', it was obvious they had neither a win or a draw.

Then we found out that 'For' and 'Against' columns must add up to the same number. In the end we put 4 in the 'For' column and 2 in the 'Against' column.

At one point we worked out the results to each match. These were:

A v B 0 - 2 B v C 2 - 2 C v D not played
A v C 2 - 2 B v D 1 - 0
A v D 2 - 0

Here is the finished table of results:

Team Played Won Drawn Lost For Against Points
A 3 1 1 1 4 4 3
B 3 2 1 0 5 2 5
C 2 0 2 0 4 4 2
D 2 0 0 2 0 3 0

Correct solutions to the problem were also sent in by:
Daniel and David from Archbishop Sancroft High School, Mary from West Flegg Middle School, Ruth from Lynn Grove High School, and students from Necton Middle School and Sheringham High School.