MathDB

16

Part of 1991 AMC 8

Problems(1)

AJHSME 1991 Problem 16

Source:

6/24/2011
The 1616 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 44?
[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("11",(0.5,3.1),N); label("22",(1.5,3.1),N); label("33",(2.5,3.1),N); label("44",(3.5,3.1),N); label("55",(0.5,2.1),N); label("66",(1.5,2.1),N); label("77",(2.5,2.1),N); label("88",(3.5,2.1),N); label("99",(0.5,1.1),N); label("1010",(1.5,1.1),N); label("1111",(2.5,1.1),N); label("1212",(3.5,1.1),N); label("1313",(0.5,0.1),N); label("1414",(1.5,0.1),N); label("1515",(2.5,0.1),N); label("1616",(3.5,0.1),N); [/asy]
(A) 1(B) 9(C) 10(D) 14(E) 16\text{(A)}\ 1 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 16