An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Find a great variety of ways of asking questions which make 8.
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?
Published October 2000,February 2011.
On a recent visit to India I was fortunate to meet
P.K.Srinivasan. He welcomed us on the 15 th August 2000
with a Magic Square which contained the date on the first row:
He explained how this can be done for any date:
There are many different solutions, and the problem is trivial
if we are allowed to repeat numbers; so the challenge is to
complete the square without using any number more than once (but
you will need to use negative numbers if the numbers in the top row
add to less than 34).
Can you complete the Christmas Day Magic Square in a different
Can you complete a magic square with the date of your birthday
in the top row?
There are some articles about magic squares on the NRICH website
which you may like to see, Magic Squares from August
1998, its follow-up Magic Squares II and also
Magic Sums and
Products . A
computer program to find magic squares shows how to program a
computer to follow the method for finding magic squares described
in this article. If this has whet your appetite there are some
problems in the Archive which you might like to have a go at
tackling (you can use the search box in the left hand margin to
P.K.Srinivasan is the Curator-Director of the Ramanujan Museum
and Maths Education Centre in Chennai (previously known as Madras).
He is very welcoming to visitors and well worth contacting if you
are ever in India (tel: 091-044-234 68 13).