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AMC 8 Math Olympiad USA Math Olympiad

Pattern Problem| AMC 8, 2002| Problem 23

Try this beautiful problem from Pattern from AMC-8(2002) problem no 23.You may use sequential hints to solve the problem.

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?

Pattern
  • \(\frac{5}{9}\)
  • \(\frac{4}{9}\)
  • \(\frac{4}{7}\)

Key Concepts


Algebra

Pattern

Fraction

Check the Answer


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

AMC-8 (2002) Problem 23

Pre College Mathematics

Try with Hints


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……..

Pattern

If we look very carefully we must notice that,
The same pattern is repeated for every \( 6 \times 6 \) tile

pattern 6/6


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

Pattern 3/3


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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