Difference between revisions of "2001 AIME I Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | In a rectangular array of points, with 5 rows and <math>N</math> columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through <math>N,</math> the second row is numbered <math>N + 1</math> through <math>2N,</math> and so forth. Five points, <math>P_1, P_2, P_3, P_4,</math> and <math>P_5,</math> are selected so that each <math>P_i</math> is in row <math>i.</math> Let <math>x_i</math> be the number associated with <math>P_i.</math> Now renumber the array consecutively from top to bottom, beginning with the first column. Let <math>y_i</math> be the number associated with <math>P_i</math> after the renumbering. It is found that <math>x_1 = y_2,</math> <math>x_2 = y_1,</math> <math>x_3 = y_4,</math> <math>x_4 = y_5,</math> and <math>x_5 = y_3.</math> Find the smallest possible value of <math>N.</math> | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=I|num-b=10|num-a=12}} | |
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Revision as of 23:24, 19 November 2007
Problem
In a rectangular array of points, with 5 rows and 
columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through 
the second row is numbered 
through 
and so forth. Five points, 
and 
are selected so that each 
is in row 
Let 
be the number associated with 
Now renumber the array consecutively from top to bottom, beginning with the first column. Let 
be the number associated with after the renumbering. It is found that 
and 
Find the smallest possible value of 
Solution
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See also
| 2001 AIME I (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 | ||
| All AIME Problems and Solutions | ||
