Puzzle Questions

A puzzle question shows a set of separate pieces and four candidate figures, and asks which figure those pieces make. The honest way to answer it is to assemble the puzzle in your head four times. That takes several minutes you do not have.

So the skill this lesson teaches is not assembly. It is elimination, and the good news is that most wrong options can be dismissed without any mental assembly at all.

Checks that cost nothing

Enlarge

Zoom in

Count

Count the pieces you were given, then count what each answer figure must be made of. They have to match.

This is the cheapest check on the subtest and it needs no spatial reasoning whatsoever.

Longest span

Measure, by eye, the longest straight distance across the finished figure. No piece can be longer than that, because every piece has to fit inside it.

A single long thin piece decides a lot of questions. If you were given a piece longer than a candidate figure's greatest width, that figure is out, and the same check works in reverse: a figure whose longest dimension far exceeds anything your pieces could span is out too.

Area

The pieces and the figure must cover roughly the same amount of space. Nobody is asking you to compute an area. A figure that is plainly twice the size of your pieces, or half of it, is wrong, and that judgment takes a second.

Distinctive features

Notches, points, curves and holes have to go somewhere. If one of your pieces has a deep notch cut into it, that notch appears in the finished figure as either an internal join or a piece of the outline. A candidate figure with nowhere for it to be is wrong.

The distinctive piece

When the cheap checks leave more than one option standing, pick one piece and follow it.

Choose the most awkward piece you were given. The longest, the thinnest, the one with the strangest angle, the only curved one, the only one with a notch.

Awkward pieces are hard to disguise. A wrong answer can fake a square or an ordinary triangle easily, because so many pieces look like those. It cannot easily fake a long thin wedge with a notch two thirds of the way along.

Find where that piece sits in each surviving figure. If it is not there, that figure is out. If it is there but at an angle the piece cannot reach by rotation, that figure is out, and the rotation lesson is where that check is worked through.

Symmetrical pieces are the worst ones to track, because a square looks the same after any quarter turn and after any reflection. Leave them alone and pick the asymmetric piece, which is also where the errors are planted.

When two options survive

They differ in exactly one thing. They always do.

Find that difference rather than re-checking both figures from scratch. Lay them side by side mentally and ask what is not the same: a piece at a different angle, an edge that is straight in one and notched in the other, a corner that is square in one and slightly obtuse in the other.

That difference is the question, and once you have found it you only have to decide which version matches your pieces.

What you can skip

Our bank holds 942 Assembling Objects questions, 482 puzzle questions and 460 connection questions - the two forms this subtest has. Every shape is flat. No question involves a solid, a measurement, a formula or an angle written as a number.

• Measuring. The wrong choices differ by a visible feature - a piece of the wrong shape, the wrong size or mirrored - not by a small difference you would need a ruler to see.
• Spatial-reasoning drills from other tests. Cube folding and 3D block rotation are different skills, and neither appears here.

Where people lose points

Trying to assemble the figure. There is not time and there is no need.

Skipping the count. It is free and it eliminates.

Tracking a symmetrical piece. It cannot be distinguished from its own reflection.

Accepting an answer because the first two pieces fit. Every option is designed so that most of it fits.

Forgetting that pieces cannot overlap. The pieces tile the figure; they do not stack.

Spending two minutes on one question. This is the lowest-value subtest on the test for an Air Force applicant, and the clock is unforgiving.

Work one in under a minute

You are given five pieces, one of which is a long thin bar noticeably longer than any other piece. Choice A is a compact square figure whose diagonal is clearly shorter than that bar. Choice B is a figure that appears to be made of four pieces. Choice C contains a bar of about the right length but lying along an edge where the given bar's notched end would have to face outward. Choice D contains the bar with its notched end inward. Which is correct, and in what order should the others fall?

D is correct, and the order the others fall in is the point of the question.

B falls first, on the count. Five pieces cannot make a figure built from four, and noticing this costs nothing and requires no spatial thinking at all.

A falls second, on span. The bar is longer than the figure's longest straight distance, so it cannot fit inside that figure in any orientation. No assembly was needed to know this.

C falls third, and it is the only one that needed real attention. The bar is present at about the right size, so the cheap checks pass it, and only tracking the notch resolves it.

Notice the economics. Two of the three eliminations cost almost nothing, and the expensive check was run once rather than four times. That is the difference between finishing this subtest and running out of clock on it.

Where this leads

Tracking the distinctive piece only works if you can tell a rotation from a reflection, which is the next lesson and the highest-value rule on the subtest.