MathDB

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:
[*]fold the top half over the bottom half [*]fold the bottom half over the top half [*]fold the right half over the left half [*]fold the left half over the right half. Which numbered square is on top after step

4

?
[asy] unitsize(18); for(int a=0; a<5; ++a) { draw((a,0)--(a,4)); } for(int b=0; b<5; ++b) { draw((0,b)--(4,b)); } label("

1

",(0.5,3.1),N); label("

2

",(1.5,3.1),N); label("

3

",(2.5,3.1),N); label("

4

",(3.5,3.1),N); label("

5

",(0.5,2.1),N); label("

6

",(1.5,2.1),N); label("

7

",(2.5,2.1),N); label("

8

",(3.5,2.1),N); label("

9

",(0.5,1.1),N); label("

10

",(1.5,1.1),N); label("

11

",(2.5,1.1),N); label("

12

",(3.5,1.1),N); label("

13

",(0.5,0.1),N); label("

14

",(1.5,0.1),N); label("

15

",(2.5,0.1),N); label("

16

",(3.5,0.1),N); [/asy]

\text{(A)}\ 1 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 16

Problem Statement