Try this beautiful problem from Algebra based on Pattern.
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?
Algebra
Pattern
Fraction
Answer:\(\frac{4}{9}\)
AMC-8 (2002) Problem 23
Pre College Mathematics
The same pattern is repeated for every \(6 \times 6 \) tile
Can you now finish the problem ..........
Looking closer, there is also symmetry of the top \(3 \times 3\) square
can you finish the problem........
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 \(\frac{4}{9}\).
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