# A mathematical challenge

• 24th January 2010, 02:32 PM
leco
A mathematical challenge
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?
• 24th January 2010, 03:08 PM
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?
• 24th January 2010, 03:15 PM
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.
• 24th January 2010, 03:19 PM
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.
• 24th January 2010, 03:47 PM
steve