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** 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 withCaroline, Gabriella, Hanna, Natalie and Rebecca all from 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:

**Thomas** , **Robert** and **Keiichi** 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** and **Luke** , also
from Moorfield, used the same method:

First we discarded $1$, $2$, $3$, $4$, $6$ and $12$. Then we knew we had six numbers left, so we counted in $5$s round the circle.

Did counting in fives work for the
second circle? **Christopher** , **Chris** and **James** found five didn't work and they:

... 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**
, 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** ,
**Elliot**
, **Anthony** , **Steve** ,
**Matt T**
, **Matt B** , **Hanah** ,
**Emma**
and **Joanne** (Phew!) all from Moorfield Junior School.
**Chris**
, **Carla** ,
**Georgia** and **Thomas** (who cleverly made a spelling circle using the name of
the school, Tattingstones). Also, well done to
**Zoe** of
Eastbury Farm School in Northwood.

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

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 twelve-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** :

Size of circle | Arrangement of letters starting at 12 o'clock going clockwise |
Number of spaces | Answer |
---|---|---|---|

7 | HANXOEG | 5 | HEXAGON |

10 | DOCONADSGE | 3 | DODECAGONS |

9 | DCNEODGOA | 7 | DODECAGON |

5 | OODVI | 3 | OVOID |

15 | TNAIRGRSIUPMALR | 4 | TRIANGULAR PRISM |

12 | DEDRCNHOEEOA | 7or19 | DODECAHEDRON |

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 $12$.