1991 AMC 8 Problem 16

Question

The

16

squares on a piece of paper are numbered as shown in the diagram. While lying on a table, the paper is folded in half four times in the following sequence:

(1)

fold the top half over the bottom half;

(2)

fold the bottom half over the top half;

(3)

fold the right half over the left half;

(4)

fold the left half over the right half.

Which numbered square is on top after step

4?

\begin{array}{|c|c|c|c|} \hline 1 & 2 & 3 & 4 \\ \hline 5 & 6 & 7 & 8 \\ \hline 9 & 10 & 11 & 12 \\ \hline 13 & 14 & 15 & 16 \\ \hline \end{array}

1

9

10

14

16

Answer: B

Concepts:paper folding process simulation

Difficulty rating: 1180

Small hint:

After each fold, track which squares end up on the bottom (or top) of the stack

Big hint:

Folds

1

and

2

leave the middle rows; folds

3

and

4

leave the middle columns, and the final left-over-right fold flips square

9

to the top

Solution:

Fold

1

(top over bottom) leaves squares

9\text{–}16

on the bottom. Fold

2

(bottom over top) leaves

9\text{–}12

on the bottom. Fold

3

(right over left) leaves

9

and

10

on the bottom.

Fold

4

(left over right) puts

10

on the bottom and brings

9

to the top.

Thus, the correct answer is B .