Difference between revisions of "2020 AIME II Problems/Problem 12"
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| − | the | + | Let <math>m</math> and <math>n</math> be odd integers greater than <math>1.</math> An <math>m\times n</math> rectangle is made up of unit squares where the squares in the top row are numbered left to right with the integers <math>1</math> through <math>n</math>, those in the second row are numbered left to right with the integers <math>n + 1</math> through <math>2n</math>, and so on. Square <math>200</math> is in the top row, and square <math>2000</math> is in the bottom row. Find the number of ordered pairs <math>(m,n)</math> of odd integers greater than <math>1</math> with the property that, in the <math>m\times n</math> rectangle, the line through the centers of squares <math>200</math> and <math>2000</math> intersects the interior of square <math>1099</math> |
Revision as of 14:58, 7 June 2020
Let 
and 
be odd integers greater than 
An 
rectangle is made up of unit squares where the squares in the top row are numbered left to right with the integers 
through , those in the second row are numbered left to right with the integers 
through 
, and so on. Square 
is in the top row, and square 
is in the bottom row. Find the number of ordered pairs 
of odd integers greater than with the property that, in the rectangle, the line through the centers of squares and intersects the interior of square 
