1985 AHSME Problems/Problem 9
Revision as of 21:08, 19 March 2024 by Sevenoptimus (talk | contribs) (Improved formatting of problem statement)
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 is the
Solution
Considering each integer modulo gives the following pattern:
We therefore observe that all numbers congruent to will appear in the second column, and since
, the answer is
.
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.