<p>A wooden cube is 3 inches long on each side and has its exterior faces painted red. If the cube is cut into smaller cubes 1 inch long each side, how many of the smaller cubes have exactly two red faces?</p>
<p>What does the question mean by exactly two red faces?</p>
<p>Thanks for your help!</p>
<p>i believe it means not one red face or three red faces.</p>
<p>Exactly 2 would mean the number of cubes on the edges of the cube, excluding the corners. Since the number of 1 inch cubes would be 27, therefore, the total number of cubes with exactly 2 red sides would be 16.</p>
<p>Is that the correct answer?</p>
<p>It means two and only two. Some would argue that a cube with three red faces could be counted because it technically has two red faces, too, so EXACTLY rules out all cubes with three, four, five, and six red faces.</p>
<p>The answer is 12. There are 8 corners with 3 reds sides. There are 6 cubes in the
center of each side with one red side and then the cube at the core with no red sides.</p>
<p>zackzm: As a follow-up to SATwriter’s point, the use of “exactly two” is related to the old joke, “How many months have 28 days?” (They all do.)</p>
<p>Thanks everyone ! The answer is 12. I finally figured out that there would be 4 cubes on each “face” with 2 red faces. 4x6 = 24 but there is a double count since the two “red faces” are not on the same “face”, the answer is 12.</p>
<p>Another view.</p>
<p>Cubes which are not on the big cube’s edges need not apply.</p>
<p>There are 12 edges, each 3 cubes long; end (corner) cubes have 3 faces painted; that leaves us with one cube per edge with exactly two red faces.
12x1 = 12</p>