Eight identical small cubes are glued together to build one larger cube. Taking all the faces of all eight small cubes together, what fraction of them can still be seen on the outside of the large cube?

Eight small cubes have $8\times 6=48$ faces in all. The large cube is 2 small cubes along each edge, so each of its 6 faces shows 4 small faces: $6\times 4=24$ are visible. The fraction is 24/48 = 1/2. A neat check: every one of the eight small cubes sits at a corner of the big cube, so each shows 3 of its 6 faces, again 1/2. The traps 2/3 and 3/4 come from guessing that 4 or 5 faces of each small cube show, which is impossible for a corner cube.