Problem:
The odd positive integers, , , are arranged in five columns continuing with the pattern shown below. Counting from the left, the column in which appears is the
Answer Choices:
A. first
B. second
C. third
D. fourth
E. fifth
Solution:
Observe that the first column consists of all numbers with value for , and that the first number in the next row beneath each value of is for the same and appears in the second column. Since appears in the second column.
Observe that all the odd integers between and appear in the first row, all between and in the second, and in general, all between and in the . Since , it follows that is the smallest odd integer in the row. Now observe that the entries in odd-numbered rows increase to the right and start in the second column.