Pacing a Run

Every other section on the PAT charges you once per question. This one charges you once per pile, then hands you the next question nearly free. Pace it like the other five and you will pay for the same drawing twice.

One analysis, two or three answers

A cube-counting figure never serves a single question. This generator gives every pile at least two questions and at most three, and a practice set will overrun the number of items you asked for rather than cut a run in half. So the moment a drawing you have not seen appears, you already know something: more questions are coming off it.

The expensive work — reading the heights, sweeping the columns, closing the tally — happens once. Everything after that is a lookup in a table you already own. Which inverts the usual advice: the way to go faster here is to spend longer on the first question of a run, not shorter.

Budget the run, not the question

PAT Foundations sets the whole-test pace at an average of 40 seconds per item across the 90 questions, and that average is the wrong unit inside this section — no cube-counting question costs 40 seconds, because the first one costs most of the run and the rest cost almost nothing.

Multiply it out and spend it lopsidedly:

Run length	Budget it carries	Spend it like this
Three questions	120 seconds	about 75 on the pile, about 15 per answer
Two questions	80 seconds	about 50 on the pile, about 15 per answer

Seventy-five seconds on one drawing feels reckless when the clock says forty per question. It is not — you are buying three answers with it. What is actually reckless is closing the first question at forty seconds with a partial count, and then spending forty more rebuilding what you threw away.

Tally everything, or score one class?

A full tally scores every cube once and files it by class, so it answers anything the run can ask. Targeted scoring counts only the class in front of you: cheaper on this question, worth nothing on the next.

Here is a pile about as expensive as this generator builds — forty-eight cubes over fourteen columns, eleven of them hidden behind their neighbors, and a run only two questions long:

On a drawing you have not seen before, always tally. There is at least one more question behind it, so the cheap option is the expensive one. Score only the asked class when you know the drawing will not come back — you have already taken the last question off it, or the clock has run down far enough that one supported answer beats two rushed ones.

That is what targeting looks like on that pile. Its second and final question asks how many cubes have five painted faces, and only the two tinted cubes matter; the other forty-six can stay uncounted. A real saving and a real gamble — and the right gamble only on the way out.

Triage when the sweep falls apart

The pile above is also where sweeps collapse. It costs the most and gives back the least, which is exactly when the temptation to start over is strongest.

Do not start over. A restart spends the entire run's budget and usually reproduces the mistake that caused it. When a sweep comes apart on a pile like that:

1. Keep the height map and the cube total. That part is cheap, you already have it, and it is what makes any later answer checkable.
2. Finish sweeping only the columns you have not committed yet, re-deriving a single column rather than the pile.
3. Answer the class your tally actually supports.
4. Flag the rest and move on. An unanswered question costs one question; a pile counted twice costs the run.

Drill by difficulty, and log misses by type

You choose the rung: the cube counting practice generator takes the difficulty as a setting, so you can sit on small piles until the sweep is automatic and then move up to the piles that actually hide cubes.

Use the explanations as a review tool, not a verdict. Each one prints the pile's cube total, how many cubes were hidden, and the complete painted-face tally — every row, not just the one you were asked about. So after a run, set your tally beside the reported one and compare row by row. Which rows moved is the diagnosis.

Then log the miss by error type, not by question number. Three types cover nearly all of them:

• Buried cube. You never counted a cube the drawing does not show. Your total lands under the height map's, and the low rows are short.
• Bottom face. You painted an underside that rests on the table. Your total is right, but every ground-level cube reads one too high, so whole rows slide up the scale at once.
• Joint double-count. You counted a face where two cubes are cemented. Total right again, but the inflation is local — a cube or two inside one column, rather than spread across the ground layer.

Both inflation errors leave the sum check satisfied, which is why the row-by-row comparison is the one that pays. Keep three columns on a page and add a tick after every missed run. After a week, the tallest column is the drill you actually need — and it will not be "cube counting", it will be one specific habit.

The takeaway

Budget the run, not the question. One drawing carries two or three questions, so a three-question run holds about two minutes of the test's pace, and the right way to spend it is most of it on the first question and a few seconds on each one after. Tally in full on any pile you have not seen; score a single class only when you know you are leaving. And when a big pile falls apart, keep the height map, answer what you can support, and flag — never recount from zero.