Copyright © University of Cambridge. All rights reserved.
'Elevenses' printed from http://nrich.maths.org/
Megan from the Thomas Deacon Academy used a
spreadsheet to find all 28 pairs of numbers that add up to a
multiple of 11. This is how she did it:
To work out the first box I started with 9, adding the rest of the
numbers, and then moved on to 46, but didn't do 46 add 9 since it
had already been done. Ithen carried this out through out the table
but making sure I had not done any in front of the number I was
working on as it would have already been done.
Then I highlighted all the answers that are in the 11 times
In the attached
are my notes.
Alex from St. Anne's School noticed
something special about the numbers in some of the
There were over 25 different pairs of numbers wich totalled a
multiple of 11.
We noticed that the numbers we added to 9, 20 and 31 were all the
The difference between 9 and 20 is 11 andthe difference between 20
and 1 is 11.
When we added 11 to 31 and made 42. We added 46, 79, 13, 90 and 2
to this number and found that each result was a multiple of
Jack and Zaim from London sent us
this very clear
explanation of why this
Curtis from Shatin College used a
similar strategy :
I divided all of the numbers by 11 and wrote down their
remainders. Then I wrote a chart of them, in the same spot. After
that, I checked in the remainder box for any pairs that added up to
11. Finally I transfered the numbers back on to the provided grid,
and came up with 28 solutions for both the 11's and the 13's.
Adil from Valentines High School
discovered the same property of the numbers that could be
We made a spreadsheet to add all the pairs in the grid and we
found a rule:
Well done to you all.
- The numbers that are of the form 11X+2 or 11X-2 will pair up to
give a multiple of 11.
- Obviously pairs of multiples of 11 will add to be a multiple of
- Finally single digit numbers will pair with another number of
the form 11X minus the single digit number itself.