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?
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
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.
This solution was submitted by
Wymondham High School
who reasoned their solution in the
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
Here is the finished table of results:
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.