This problem encouraged a huge number of responses. There were different strategies used to solve the problem and many suggestions for other words that could be used to make a spelling circle.

Chen Kaizhen, used the guess and check method for problem solving. Chen explains, "I moved randomly.... which eventually led me to the answer ". This can work quite well, but sometimes you have a hunch there is a method or piece of information that will help you. This happened with Caroline Foster, Gabriella Grey, Hanna Malloy, Natalie Poon and Rebecca Sherwood all from Year 7, The Mount School. "We think it has something to do with 5 and 7 not going into 12."

In fact as the members of Burgoyne Maths Club wrote:
"We think that the rule is that if you use factors you go back to where you started and the same thing happens with multiples. The number of spaces you move must NOT be a FACTOR or a MULTIPLE of the SIZE of the CIRCLE."

Thomas Squires, Robert Lyons and Keiichi Isayama from Moorfield Junior School, used what they know about multiples:
"We got rid of the multiples of twelve because (when we counted spaces we) would have kept on going to the same spaces/letters all the time." Richard Frost and Luke Pilsbury, also from Moorfield, used the same method: "First we discarded 1,2,3,4,6 and 12. Then we knew we had 6 numbers left, so we counted in 5's round the circle."

Did counting in fives work for the second circle? Christopher Barratt, Chris Doherty and James Knot found five didn't work and "...decided to count on in sevens because it is not a multiple of twelve." All of the people who sent in their solutions agreed with these boys.

But was there a second solution? Ruth Roberts, a pupil at Balderstone Primary School in Blackburn, wrote that she had found five and seven worked but having tried other numbers Ruth reports: "We couldn't do it any other way".

Thank you for your solutions, explanations and willingness to be mathematical problem solvers: Adam Knowles, Elliot Sutcliffe, Anthony Hayward, Steve Townsend, Matt Tattler, Matt Barker, Hanah Fahey, Emma Powis, and Joanne Langford (Phew!) all from Moorfield Junior School. Chris Black, Carla Theobald, Georgia Barton and Thomas Harley (who cleverly made a spelling circle using the name of the school, Tattingstones). Also, well done to Zoe Kantor of Eastbury Farm School in Northwood.

Oh yes, so what were the words? Over to Ruth Roberts:

The first one is MATHEMATICAL counting in fives
The second one is MEASUREMENTS counting in sevens.

Here are some words sent in by the readers above. Put the letters to put into a 12-section circle with the first letter in the 12 o'clock position and see if you can discover what they are.

I, C, T, I, R, N, E, N, T, E,O, S (It's a word out of a maths dictionary)
D, A, O, E, D, O, H, N, C, R, D, E
I, U, D, L, V, Y, D, N, A ,E, L, I
G, H, O, C, R, L, P, E, I, G, A, A

These final ones are the same word but using a different ** in each case.
D, C, E, F, L, I, C, S, I, T, F, U
D, L, F, I, I, S, U, I, T, F, E, C

Here are series of possible words from Burgoyne Maths Club:

Let me leave you with this question: If the spelling circles don't work with multiples of 12, will they also work when counting by 8, 9, 10 or 11? After all, they are not factors of 12.