Quandaries and Queries


Hi my name is Rebecca and I am in grade 6

my maths question is use the numbers 1,2,3,4,5,6 and 7 place each number in a circle so each line adds up to 12. There are seven circles, six on the outside and one in the middle. Each number lines up with the middle number and the outside numbers line up with the one directly across from it as if a line was going through the middle number circle.

Rebecca Cox.



Hi Rebecca,

I looked at the list of numbers that you have

1 2 3 4 5 6 7

and I know that you are looking for an arrangement with 6 numbers around the outside of a circle and one in the middle. You want to line up triples of numbers, two on the outside and the one in the middle so that the sum is always 12.

What I see from the list above is that:

  • if you add the largest and smallest you get 8 (1+7=8),
  • if you add the second smallest to the second largest you get 8 (2+6=8),
  • if you add the third largest to third smallest you get 8 (3+5=8).

You are left with 4 and 8+4=12.

Hence if you put the 4 in the middle and pair the 1 and 7, the 2 and 6 and the 3 and 5 you will get what you want.




Go to Math Central