Only 4 colours needed

You probably get the Nobel prize if you find a gentle proof that you need only 4 colours to colour the entire map of the world or a globe. Yes, it seems that only 4 colours are needed and no neighbouring countries will have the same colour.

What's the story

1852. Frederick Guthrie had a brother: Francis and Francis had a problem. He could colour any map with only 4 colours and no neighbour area on that map would have the same colour. But how to prove that? So Frederick, who studied at the University College in London, went to his professor in mathematics De Morgan and told him about his brother's theory. De Morgan didn't even know that 4 colours were enough and passed the question the same day to another mathematician in Dublin: Hamilton. Hamilton responded that he had no time for that sort of a question, so De Morgan started to ask everyone to solve this 4 colour theorem.

The theory is simple and explainable to anyone, but finding proof seemed far from easy: 27 years later, on July 17, 1879, Alfred Kempe announced in Nature that he had a proof of the "Four Colour Conjecture". All mathematicians happy at last: somebody finally had find a solution for such a simple problem. Kempe was elected a Fellow of the Royal Society and was even knighted a few years later.

Oops, in 1890 a fellow called Percy Heawood discovered there was a defect in Kempe's proof. Now all mathematicians around the world felt the shame that they were fouled for 11 years. And shame was not their only problem: they had to start all over again to find proper proof. Heawood himself studied for another 60 years trying to find a neat solution. But he didn't.

Eventually it took more than a century: In 1976 the complete solution to the Four Colour Theorem was found, but the proof was no conventional proof at all: it was the first major theorem to be proved using a computer. So a proof that could not be verified directly by other mathematicians.

So, if you have that proof that is made of traditional logical steps, you are more than welcome to tell us. You might even get knighted.

Make 10 lines

Thanks to a clever random generator you get an unlimited amount of puzzle games. And depending on your mood you can choose from 6 different levels.

What's the story

The aim was a puzzle game, without a competing element: So the puzzle in front of you is your puzzle and your puzzle only. You can also choose the level of difficulty you prefer:

• If you are in the mood for no thinking at all: choose RELAX or EASY.
• Do you want to set your mind to something else: choose MEDIUM or TRICKY
• Are you in for a challenge? Try HARD or even DIABOLIC

A simple puzzle game with only 32 puzzle pieces. But together they are good for 892.616.806.656.000.000.000.000 possible combinations. For you to find the 1 solution.

There are 100 levels from simple to extremely hard, but do not worry: if you think a game is too hard then you can always use one of the three hints available at any level.

• Swipe to turn the ball.
• Tap on the ball to turn the puzzle piece.
• Tap and hold a while if you are sure the puzzle piece is in the right position. The blue line will turn green.
• Too difficult? Tap on the "3H" button and then on a puzzle piece. It will turn red and turn in the right position. You get 3 hints in every game.
• Use two fingers to zoom in or out.

What's the story

I was surprized myself that I made Loop Loop first, which has 180 puzzle pieces followed by One Line Weekly which has even more than one thousand puzzle pieces. Apparantly I had to invent these "difficult" games before I could make this relatevily simple Lonely Line with only 32 puzzle pieces. But simple might not be the right word here. Because, with only 32 puzzle pieces, a Lonely Line puzzle can be even harder than a One Line Weekly. Good luck.