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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