Bunuel wrote:

What is the number of squares of perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned?

(A) 2

(B) 4

(C) 8

(D) 32

(E) 72

Attachment:

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To find the number of squares with perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned:

Squares with perimeter of 36 have side length 9

1. Sketch

---a rectangle with length 72 and width 36

---a few squares with side length 9 adjacent to one another, a few going across, a couple going down

It soon becomes evident (no need to draw the rest):

With 9 as each square's side length, 8 squares will fit inside the rectangle's length and 4 will fit inside its height, 8 * 4 = total 32

OR

2. Divide rectangle side lengths by square side lengths, then multiply what are essentially columns and rows

Rectangle length 72/9 = 8 squares on long side

Rectangle width 36/9 = 4 squares on short side

8 * 4 = 32 squares will fit into a partitioned rectangle

ANSWER D

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In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"