Difference between revisions of "2002 AMC 8 Problems/Problem 11"
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==Solution 2== | ==Solution 2== | ||
− | The edge of each square is one tile length longer than the edge of the previous square, which means that each square has <math>2*</math> edge length <math>- 1</math> more tiles than the previous square, because each square is just one edge added on the top and on the right to the previous square, with one overlapping tile. Then the seventh square has <math>2 | + | The edge of each square is one tile length longer than the edge of the previous square, which means that each square has <math>2*</math> edge length <math>- 1</math> more tiles than the previous square, because each square is just one edge added on the top and on the right to the previous square, with one overlapping tile. Then the seventh square has <math>2^27-1=13</math> more tiles than the sixth square, which is <math>\boxed{\text{(C)}\ 13}</math>. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2002|num-b=10|num-a=12}} | {{AMC8 box|year=2002|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 12:39, 26 October 2016
Contents
[hide]Problem
A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?
Solution
Solution 1
The first square has a sidelength of , the second square , and so on. The seventh square has and is made of unit tiles. The sixth square has and is made of unit tiles. The seventh square has more tiles than the sixth square.
Solution 2
The edge of each square is one tile length longer than the edge of the previous square, which means that each square has edge length more tiles than the previous square, because each square is just one edge added on the top and on the right to the previous square, with one overlapping tile. Then the seventh square has more tiles than the sixth square, which is .
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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