The Right Face, the Wrong Way Round

Right face, right shade, wrong way round

This is the quietest wrong answer in the section. Every marking is on the face it belongs on. Every shade is the shade the pattern printed. Every neighbour is the neighbour the fold produces. The only thing wrong is that one marking has been turned in place — a quarter, a half or three quarters of a turn about the centre of its own face.

None of the checks that beat the other families touch it. Counting shaded faces passes it. Naming which shade sits beside which passes it. Checking which two faces are back to back passes it. The trap is invisible unless, while you were folding, you tracked something finer than a face.

Where it can appear at all

A marking has to have a direction before it can point the wrong way, so this trap only exists on markings that cover part of a face:

• A shaded half — the half hugs one of the four edges, and turning the face moves it to another edge.
• A shaded triangle — its diagonal runs one way or the other, and its right angle sits in one of four corners.
• Die faces that carry a direction — the 2, the 3 and the 6.

A face filled edge to edge in one shade has nothing to rotate: turn it and it draws the same square. That is not a matter of taste but of what a wrong answer is allowed to be — an option that turns a symmetric marking reproduces the correct solid exactly, and a wrong option is never allowed to be the right answer seen from another angle, so the engine drops it. The same logic rules out the die's 1, 4 and 5, which are unchanged by a quarter turn. Only markings that look different after turning can carry this trap.

What it looks like

Here is a pattern with two part-face markings, and the solid it folds into:

The pattern

The correct cube

Now the same solid with the black half on the top face turned a quarter — same face, same shade, same size, pressed against a different edge:

Trap — the half against the wrong edge

And the version that turns the triangle on the side face instead, swinging its diagonal the other way:

Trap — the diagonal the wrong way

Put the three drawings beside each other and the difference is obvious. In an item you get one of them, among four options, at a size like these, and there is nothing labelled to compare against. That is why this family is the one that decides hard items.

The die version

Pips make the same trap arithmetic-proof: the count on the face is untouched, so the only thing that changed is which way the pattern of pips runs.

The 2 and the 3 are built along a diagonal, so a quarter turn swings that diagonal from one corner pair to the other. The 6 sits in two lines of three, and a quarter turn stands them up the other way. Read those three numbers as shapes with a direction, not as counts, and the trap becomes visible; count the pips and it will pass straight through.

The cure is a habit, not a technique

There is no new trick here. The fix is the one from the anchor-face lesson, applied one level finer: when you fold, track an edge, not a face.

1. Pick the marked cell on the pattern and name the edge its shading touches — the edge it shares with a specific neighbouring cell.
2. Fold that neighbour up. The shaded edge now touches that neighbour's face on the solid, and it will keep touching it whatever else you do.
3. Judge each option by that contact alone: does the shaded half meet the neighbouring face, or does it meet a different one?

An edge contact survives every rotation of the whole solid, so you can check it from any angle the option happens to be drawn at. A remembered picture of "black half on top, roughly to the left" does not survive, which is exactly what the trap is built to exploit.

One caution when you drill this. If an option's marking sits on the wrong face entirely, or if every marking is correctly placed but the whole solid reads back to front, you are looking at a different family and a different check — those were the two previous topics. This one is settled only after you have confirmed that each marking is on its own face. Build the habit on the pattern folding practice generator at medium and hard, where half-face and diagonal shading appear.

The takeaway

The subtlest wrong answers keep every marking on its correct face and simply turn one of them in place. Only markings with a direction can carry it — a shaded half, a diagonal triangle, a 2, a 3 or a 6 — because turning a symmetric marking would reproduce the correct solid. Catch it by tracking which edge of a shaded region touches which neighbouring face as you fold, and judging every option by that contact rather than by a remembered picture.