Difference between revisions of "1985 AHSME Problems/Problem 9"
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− | The odd positive integers <math> 1, 3, 5, | + | The odd positive integers <math> 1, 3, 5, 7, \cdots </math>, are arranged into five columns continuing with the pattern shown on the right. Counting from the left, the column in which <math> 1985 </math> appears in is the |
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Revision as of 18:07, 15 December 2011
Problem
The odd positive integers , are arranged into five columns continuing with the pattern shown on the right. Counting from the left, the column in which
appears in is the
Solution
Notice that the pattern repeats every terms. Therefore, we only have to consider the first
terms. Also, since each term adds
to the previous term, the pattern repeats every
natural numbers. Thus, notice that all numbers
is in the first row, all numbers
are in the second row, and so on.
Notice that since , it's in the same row as
, which is the fourth row,
.
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |