A mathematical challenge

[leco]

Anyone know anything about maths? Here's a puzzle for you:

 

A floor is decorated with a tiled mosaic. The whole mosaic is a regular pentagon. It is made from 4 types of tiles. The length of the side of the whole mosaic is just over 6 times the length of the side of one pentagon tile.

 

How many of each type of tile make up the mosaic?

 

Question: How is this worked out mathematically? Is it a formula of some sort or just a case of playing around with pentagon shaped tiles?

[steve]

A true pentagon (all angles / sides the same) doesn't tessellate and couldn't be used alone to make a mosaic floor.

 

It can be done like this: Shapes that tessellate - irregular pentagon grid

 

Or should it be hexagons?

[leco]

The details do not say that all of the tiles are pentagons, only that the whole is a regular pentagon. As you say pentagons do not tessellate alone, so I'm guessing that one or more types of tile are not pentagonal. Types of tile may just mean colour rather than shape. So there could for example be red and green pentagons and red and green diamonds.

 

Also tessellated irregular pentagons would not make a regular pentagon.

Edited January 24, 2010 by leco

[mjs_mjs]

I thought that it wouldn't work with regular pentagons alone ither. I guess this is just too openended a question to solve.

[steve]

My bad, read the question wrong.

[leco]

Incidentally this is supposed to be a Year 7 maths challenge! I have no idea where to start:(