1998 AMC 12 Problem 1

Question

Each of the sides of five congruent rectangles is labeled with an integer, as shown. These five rectangles are placed, without rotating or reflecting, in positions

I

through

V

so that the labels on coincident sides are equal. Which of the rectangles is in position

I?

A

B

C

D

E

Answer: E

Concepts:logic edge matching

Difficulty rating: 1430

Small hint:

The rectangle in position

II

must match another rectangle on both vertical sides

Big hint:

After finding position

II

, match its left label to the right label of position

I

Solution:

Position

II

needs both its left and right labels to occur as right and left labels, respectively, on two other rectangles. Only

D,

with side labels

7

and

4,

permits both matches:

E

has right label

7,

and

A

has left label

4.

Hence position

I

contains

E,

so the correct answer is E.