## December 31, 2007

### CMYK should be fine

This map lead to a conjecture in graph theory in 19th century which till now has not been proved “properly”. Although computerized exhaustive search proofs exist, mathemeticians reject it by calling it a “telephone directory” and they want the proof to be a “poem”.

Identify the conjecture/theorem/problem.

**Happy New Year!**

Cracked by: udupendra(Congratulations on scoring a century!) , jayanth , madhur , Dibyo , shenoyvarun86 , sumanth , sidsen , Ranjana Ninan , Shreyas , Keerthi , VikraM , piezocake , BiGFooT , nishas thambi , Gammafunction , prasanth , yaksha , Poornima , bobo , shashank and Arjun Chennu.

Answer:

Quoting Arjun Chennu,

This is the Four Colour Problem identified by Francis Guthrie in 1852, when it was ‘discovered’ that any map could be colored using 4 colors such that adjacent segments received different colors.

Four Colour Theorem – this is truly a New Year’s gift!

The four color theorem (also known as the four color map theorem) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent only if they share a border segment, not just a point. Each region must be contiguous: that is, it may not have exclaves like some real countries such as Angola, Azerbaijan, or the United States.

It is often the case that using only three colors is inadequate. This applies already to the map with one region surrounded by three other regions (although with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map.

The four color theorem was the first major theorem to be proven using a computer, and the proof is not accepted by all mathematicians because it would be unfeasible for a human to verify by hand (see computer-assisted proof). Ultimately, in order to believe the proof, one has to have faith in the correctness of the compiler and hardware executing the program used for the proof.

The perceived lack of mathematical elegance by the general mathematical community was another factor, and to paraphrase comments of the time, “a good mathematical proof is like a poem—this is a telephone directory!”

happy new year! *hic*

Four Color Theorem (also known as the four color map theorem)

I’m guessing this is the four-colour conjecture of topology.

the Four Colour theorem-a theorem stating that only 4 colors are enough to distinguish the regions in a plane/map!

Its(the proof) not a poem because it is highly impossible to prove by actually colouring a region by hand

Its a telephone directory because no one can verify a directory,one can just believe it..

1)The Four Colured theorem.

The conjecture was proposed by Francis Guthrie while trying to color the map of england.

four colour theorem

4 colour map theorem

Four colour theorem.

The theorem was “four color theorem” first proposed in 1852 by Francis Guthrie. wiki: http://en.wikipedia.org/wiki/Four_color_theorem

the four colour theorem…. only 4 colours are sufficient to colour a map(say) such that no 2 regions sharing a border have the same colour representing them….

The 4-color theorem.

The 4 – Color Theorem , which was 1st proposed in 1852 by Francis Guthrie while he was trying to color the map of counties of England ( as shown in the pic ) & noticed that only four different colors were needed.

the four colour theorem

The Four Colour Theorem

A very happy new year to all of you here at Boiledbeans!

The 4 color theorem – It has the distinction of being the first major theorem to be proved using a computer.

The theorem states that any plane separated into regions, such as a map of countries or states, can be colored with only four colors, such that no adjacent regions have the same color.

Four color theorem

Four color theorem

4 colour theory

Four color theorem – given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color.

This is the Four Colour Problem identified by Francis Guthrie in 1852, when it was ‘discovered’ that any map could be colored using 4 colors such that adjacent segments received different colors.