Pattern Problem| AMC 8, 2002| Problem 23

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 $\frac{4}{9}$ .

Other useful links

Related

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 $\frac{4}{9}$ .

Other useful links

Related

Leave a ReplyCancel reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

HALL OF FAME BLOG OFFLINE CLASS

CHEENTA ON DEMAND BOSE OLYMPIAD

Cheenta Academy Private Limited |

support@cheenta.com

Menu

Math Olympiad Program