What an Option Actually Shows You

Three faces, and three you cannot see

A drawing of a cube shows exactly three faces. The other three are behind it, and nothing in the drawing so much as hints at what they carry. Everything about how you read the four options follows from that.

The pattern

Three faces in view

The pattern on the left fixes all six faces. The drawing on the right commits to three of them — black on top, gray on the right, stipple on the left — and says nothing whatsoever about the rest.

The same solid, turned

The four drawings in an item are not taken from one camera position. Each is the solid posed at whatever orientation it was drawn at, so two options can show completely different sets of faces. Here is the identical cube from the figure above, twice more:

The same cube, turned

The same cube, turned again

Different faces in view, different amounts of shading in view — and, face artwork aside, exactly the same drawing. That is not a coincidence of these two poses: every drawing of a cube has the same hexagonal outline, so on a cube item the outline carries no information at all. On the other solid families the options are posed at different angles, which changes the outline without telling you which pose is the right solid. Either way, matching an option by its overall shape is worthless. The artwork on the faces is the only evidence.

What a missing mark proves

Nothing. In the last drawing, two of the three marked faces are turned away. The drawing is not wrong for hiding them, and — this is the part that costs people points — it cannot be eliminated on a face it does not show. If the relationship you were testing involves the gray face or the stippled one, that drawing is simply silent on your test. Find a pair of faces it does show and test that instead.

There is a limit to how far that runs, and it cuts the other way. Every drawing is posed to put as much of its own marking in view as it can: the answer is drawn at an orientation that shows as many marked faces as any orientation of that solid allows, and every wrong drawing has to show enough of its marking to be judged at all. So the number of shaded faces you can see is not what separates them. Counting shades is not a check. Reading them is.

Read the disagreement before you fold

Put those together and the opening move of an item is not folding — it is reading. Look across the four drawings and find the one thing they disagree about, because that is the only thing worth folding the pattern to settle.

Which cube results when the pattern is folded into the page?

A

B

C

D

Start with what is constant. All four drawings have the same outline, and all four show two shaded faces, so neither the shape nor the count is doing any work here. What is left is the artwork: which shade sits on which visible face, and which edge each shade leans on. That is the disagreement, and it names the check. Then, and only then, go to the pattern and settle it — one relationship, not six faces.

Do this on every item you generate in the pattern folding practice generator, even the ones you are sure of. Reading first is a habit, and it is the habit that pays for itself on the hard items.

The takeaway

An option shows three faces and hides three, so it can only ever make three faces' worth of claims. Options are posed independently, so the outline is never the evidence — on a cube it is the same hexagon every time. A mark you cannot find may just be turned away, so nothing can be eliminated on a face it does not show, and the number of visible shades separates nothing. Read what the four drawings disagree about first; fold only enough to settle it.