Four Colour Map (Posted on 2008-07-08)

This array, which I have begun to colour, is the top part of a "Four Colour Map" with rows extending beyond the borders given.

The boundaries displayed in Rows 1 to 4 are repeated down the map, ie, Row 5 has the same boundaries as Row 1, but may be coloured differently.


In colouring this map no two regions of the same colour may have part of a border in common and a row pattern is repeated across the row.

Tasks:
1. At which row could I soonest expect to see the exact colouring and layout pattern of Row 1?

2. Suggest a topologically simpler and what probably is a more aesthetic geometric layout for the vertices of my map?

	Submitted by brianjn
Rating: 5.0000 (1 votes)
Solution:	(Hide)
Part 1. In Row 3 use the same colours as in Row 1 but interchange the positions of Colours 2 and 3. Colour the small rectangles in both Rows 2 and 4 with the Colour 1, and then in Row 2 alternate Colours 2 and 4, but in Row 4 alternate Colours 3 and 4. Part 2. Consider an equilateral triangle with its angle bisectors meeting at its centre, and around each vertex and the centre describe a small circle: O /*\ / * \ / O \ / * * \ / * * \ O-----------O Use this layout of 4 circles and the six lines which create this network to tessellate the plane. Each circle is either linked to one of 12 others, or one of 3. The large red rectangle, labeled 1 in the problem, is equivalent to a circle which is the hub of 12 circles. The small rectangle beneath the green rectangle, labeled 3, is equivalent to a circle which is the hub of 3 circles. The triangles are equivalent to the other areas in the problem's diagram.

	Subject	Author	Date
	re: Solution to Task 1 - hiccup	brianjn	2008-07-09 05:45:33
	Solution to Task 1	Dej Mar	2008-07-08 19:28:08