1985 AMC 12 Problem 9

Question

The odd positive integers,

1,

3,

5,

7,

\ldots,

are arranged in five columns continuing with the pattern shown. Counting from the left, the column in which

1985

appears is the

\begin{array}{ccccc} &1&3&5&7\\ 15&13&11&9&\\ &17&19&21&23\\ 31&29&27&25&\\ &33&35&37&39\\ 47&45&43&41&\\ &49&51&53&55 \end{array}

first

second

third

fourth

fifth

Look at the entries that begin each left-to-right row

Relate

1985

to a nearby multiple of

16

The last number in each right-to-left row is

16k-1,

and the next row begins with

16k+1

in the second column. Since

1985=16\cdot124+1,

it begins such a row and lies in the second column.

Thus the correct answer is B.

Problem 9 in other years