How Difficulty Scales

A hard pile is not a small pile with more cubes on it. Three settings move together, and the third one changes which questions you are asked.

Three dials, turned at once

The generator widens the footprint, raises the ceiling on each column, and raises the floor on the total, all in the same step. Here is the whole configuration, with the pile sizes it actually produces:

Setting	Small	Medium	Large
Footprint	3 × 3 columns	4 × 3	4 × 4
Tallest column allowed	2	3	4
Cubes, floor	6	10	14
Cubes, measured	10.3 average (6–17)	19.4 (10–33)	31.2 (14–48)
Cubes hidden from view	0.9 average, in 65% of piles	2.8, in every pile	4.8, in every pile

The measured rows come from running the generator over the first 4,000 seeds at each difficulty; the ranges are what those samples produced, not hard ceilings. A large pile carries about three times the cubes of a small one, on a footprint with nearly twice the columns.

Hidden cubes stop being optional

A cube is hidden when all three of the faces the drawing would have shown you — its top and the two that turn toward you — are covered by neighbors. On small piles the generator does not care whether one exists; it happens in about two thirds of them. On medium and large piles it rejects any arrangement that produces none, so every medium and large pile has at least one cube you can only infer. The average large pile has just under five.

One fact about those cubes is structural, not statistical. A hidden cube has three of its five paintable directions blocked by the very neighbors that hide it, so it can carry two painted faces, one, or none — never three or more. Over 3,000 piles at each difficulty, no hidden cube ever scored above two. When a question asks about a low number on a big pile, the cubes you cannot see are part of the answer.

The answer ladder decides what can be asked

Every item you will drill here offers the same five choices: one cube through five cubes. That fixes a hard ceiling on what is answerable. A painted-face class can only be asked about when the pile holds at least one and at most five cubes in it — hold six, and no choice on the screen is correct.

The generator enforces exactly that. It tallies the pile, keeps only the classes holding one to five cubes, and throws the pile away entirely if fewer than two classes survive. Every question you see was filtered through that test before it reached you.

Small piles: the middle is live

Ten cubes, and the tally reads one cube with a single painted face, three with two, three with three, two with four, one with five. Every row sits inside one-to-five, so all five classes pass the filter and any of them can be asked. The middle of the ladder is also where most of the cubes are — which is why, on small piles, that is mostly what you get asked. Across 4,000 small piles, the two- and three-face classes took 63% of all questions.

Large piles: the middle is locked out

Thirty-three cubes. The badges label every cube you can see; four cubes carry no badge because they are hidden, and between them they hold one painted face, two, two, and two. The full tally is three cubes with one painted face, nine with two, fourteen with three, five with four, two with five.

Now apply the filter. Nine and fourteen are both past the top of the ladder, so the two- and three-face classes — twenty-three of the thirty-three cubes — cannot be asked about at all.

This is not a quirk of one pile. Across 4,000 large piles, the two-face class overflows the ladder 88% of the time and the three-face class 87% of the time. What is left is the sparse end of the distribution:

So the asked numbers invert. On small piles the reason a class cannot be asked is almost always that it is empty (3,832 empty against 336 overcrowded, across every class of every pile). On large piles the reason is almost always that it is crowded (9,705 overcrowded against 105 empty). The questions follow:

Asked about…	Small piles	Large piles
one painted face	20%	26%
two	31%	5%
three	32%	5%
four	15%	28%
five	2%	37%

On a large pile, expect to be asked about the extremes: the few cubes standing almost free, and the few that are nearly walled in. Nine questions in ten land there. The one-face class is where the nearly-walled-in cubes live — on large piles, 47% of one-face cubes are hidden from the drawing.

Why large piles often carry only two questions

A run is as long as the pile has askable classes, capped at three. Small piles almost always keep at least three classes inside the ladder, so they fill the cap: 97% of small piles carry three questions. Large piles routinely lose both the two- and the three-face class to overcrowding, and when that happens only two classes are left standing. 53% of large piles carry two questions instead of three. The pile that costs you the most analysis is the one least likely to pay you back three times.

What this is, and what it is not

Everything above is measured from this generator, whose difficulty settings are the table at the top of this page. It is real and it is stable, and it tells you what to expect when you drill here. It is not a published property of the exam: no one has stated how the live test scales its piles, so treat this as calibration for your practice, not as a prediction you would bet an answer on. If the settings change, this page changes with them.

The takeaway

Difficulty scales on three dials at once — wider, taller, denser — and every medium or large pile hides at least one cube. Because the choices only run from one cube to five, a class holding six or more can never be asked, and on a large pile that silently removes the crowded middle of the tally. Drill large piles expecting questions about the most exposed cubes and the most enclosed ones, and expect two questions off that pile more often than three.