Try this beautiful problem from Algebra based on Pattern.

## Pattern – AMC-8, 2002- Problem 23

A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?

- \(\frac{5}{9}\)
- \(\frac{4}{9}\)
- \(\frac{4}{7}\)

**Key Concepts**

Algebra

Pattern

Fraction

## Check the Answer

But try the problem first…

Answer:\(\frac{4}{9}\)

AMC-8 (2002) Problem 23

Pre College Mathematics

## Try with Hints

First hint

The same pattern is repeated for every \(6 \times 6 \) tile

Can you now finish the problem ……….

Second Hint

Looking closer, there is also symmetry of the top \(3 \times 3\) square

can you finish the problem……..

Final Step

If we look very carefully we must notice that,

The same pattern is repeated for every \( 6 \times 6 \) tile

Looking closer, there is also symmetry of the top \( 3 \times 3\) square,

Therefore the fraction of the entire floor in dark tiles is the same as the fraction in the square

Counting the tiles, there are dark tiles, and total tiles, giving a fraction of \(\frac{4}{9}\).

## Other useful links

- https://www.youtube.com/watch?v=YKtaNTxWA64
- https://www.cheenta.com/circles-and-semi-circles-amc-8-2010problem-23/

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