The total surface area of the three cubes (before any gluing occurs) is 96 + 24 + 6 =126. Glue the cubes so that one face of the medium size cube is entirely contained in one face of the largest cube. Then glue on the smallest cube so that two of its faces are entirely contained in the faces of the other two. The resulting surface area is 126 – 2(4) – 2(1) – 2(1) = 114.

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