We are pupils in a 6.grade on Skovboskolen. Our school is in Bjaeverskov on Zealand which is a part of Denmark. Our school is 50 km to the south of our capital, which is Copenhagen. You can see a picture of our school on our website (www.skovboskolen.dk).

Here it is: Our mathsteacher Lise Vikkelsoe asked us around christmas, if we thought it would be fun to work with something, she called the four-colour problem. OK! We said.

We began doodling on a piece of paper without lifting the pencil. The exercise was to colour the closed partitions that appeared with as few colours as possible, and the following rule applied that two identical colours must not join eachother.
OK! We could do that! - We agreed! - We found a rule! Our mathsteacher is very much into that.

Question : Can you find that rule too?

We carried on, and now we were allowed to lift the pencil from the paper. And what happened? Some times we had to use 3 colours and some times 4 colours.

Question : Can you figure out, when you can do with 3 colours, and when it is necessary with 4 colours? A rule as a matter of fact.

Then the best thing happened. We went to a part of the school, where we have 14 computers. Here we produced after the same principles the drawings in Paint. It was much quicker to colour the drawings that way.

Now the funniest thing happened. Because Lise said that is was always possible to colour a drawing with 4 colours after those principles. But... we have made some drawings, that demands 5 colours, and she has tried it once and she only used 4!
If it is true that you can`t do with only 4 colours, she has promised us cream puffs and on top of that she said, that we will be worldfamous in Denmark, because since the question was asked in 1852 for the first time, no mathematician has been able to prove that it was like this, but also there has been no one, who has made a drawing, that demanded 5 colours.

Question : Can you colour our drawings with only 4 colours?

Challenge : Try to send us some "difficult" drawings, and let us try yours!

We give you Lises mail-adress, but if you use our name, we can answer you ourselves, because we are improving our English too.