PN Cadet Non-Verbal Intelligence Syllabus

For a vertical mirror placed to the right/left of an object, which directions are swapped?

Left and right are interchanged (lateral inversion); top and bottom remain unchanged.

In a mirror image, how does the letter 'b' typically appear?

As 'd' (left-right reversed); for example, the mirror image of 'b' looks like 'd'.

Which capital letters look the same as their mirror image (vertical mirror)?

Letters with vertical-axis symmetry: A, H, I, M, O, T, U, V, W, X, Y.

What is a Water Reflection (water image) in non-verbal reasoning?

The image formed when an object is reflected in water below it; the figure is inverted top-to-bottom (upside down) while left and right stay the same.

In a Water Reflection, which directions are swapped compared to a mirror image?

Water image inverts top and bottom (vertical flip); a mirror image inverts left and right (horizontal flip).

Which digits remain unchanged in their water reflection?

Digits with horizontal-axis symmetry, notably 0, 1 (in plain form), 3, and 8 appear nearly the same when flipped top-to-bottom.

How does the letter 'B' appear in its water reflection?

It appears flipped vertically (upside down), so the two bumps point downward; B does not look the same in water image because it lacks horizontal symmetry in standard form.

What axis of reflection does a mirror image use versus a water image?

Mirror image reflects across a vertical axis (left-right reversal); water image reflects across a horizontal axis (top-bottom reversal).

In 'Image of Letters and Numbers', why can rotation be confused with reflection?

Because some symmetrical characters (like O, X, 8) look identical under rotation and reflection, but most do not, so you must apply the exact required operation (mirror, water, or rotation).

How does the number '2' appear as a mirror image?

It appears laterally reversed, like a backwards '2' (its curve opens toward the opposite side).

Which capital letters read the same after a 180-degree rotation?

Letters with point (rotational) symmetry: H, I, N, O, S, X, Z.

What is a Rotated Figures problem?

A figure is turned by a certain angle about a point, and you must identify how it looks after rotation, or by what angle/direction it was rotated.

What is the difference between clockwise and anticlockwise rotation in figure problems?

Clockwise rotation turns the figure in the direction of clock hands (right-to-down); anticlockwise (counterclockwise) turns it the opposite way (left-to-down).

A figure rotated 90 degrees clockwise then 90 degrees clockwise equals what single rotation?

A 180-degree rotation (the figure ends up upside down/inverted).

When tracking a rotated figure, what reference helps confirm the angle?

Follow a distinctive marker (an arrow, dot, or odd corner) and measure how far it has turned from its original position to confirm the rotation angle and direction.

What is the Paper Folding and Cutting (paper cutting) problem type?

A sheet of paper is folded one or more times, then cut/punched; you must determine how the paper looks (the pattern of holes/cuts) when unfolded.

What symmetry principle governs the unfolded pattern in paper folding and cutting?

Each cut/hole is mirrored across every fold line, so the final unfolded pattern is symmetric about each crease the paper was folded along.

If a paper is folded once and one hole is punched through both layers, how many holes appear when unfolded?

Two holes, positioned symmetrically (mirror images) about the fold line.

If a square paper is folded twice (into quarters) and one hole is punched, how many holes appear unfolded?

Four holes, one in each quarter, arranged symmetrically about both fold lines.

What is the rule for the position of holes relative to a fold line when unfolding?

Holes appear at mirror-image positions: a hole at distance d from the fold reappears at distance d on the opposite side of that fold line.

What is a Cubes problem (cube folding/painting) in non-verbal reasoning?

Problems involving a cube — either folding a flat net into a cube to find opposite faces, or analyzing a painted cube cut into smaller cubes.

In a standard cube, how many faces are adjacent to any given face, and how many are opposite?

Each face is adjacent to 4 faces and opposite to exactly 1 face.

In a cube net (unfolded cube), how do you identify opposite faces?

Faces that are one square apart in a straight line on the net (separated by exactly one face) are opposite; adjacent squares on the net become adjacent faces, not opposite.

If a painted cube is cut into n x n x n smaller cubes, how many small cubes have exactly 3 painted faces?

Always 8 (the corner cubes), regardless of n (for n greater than or equal to 2).

For an n x n x n painted cube, how many small cubes have exactly 2 painted faces?

12 x (n - 2), the cubes along the edges but not at corners.

For an n x n x n painted cube, how many small cubes have exactly 1 painted face?

6 x (n - 2)^2, the cubes at the center of each of the six faces.

For an n x n x n painted cube, how many small cubes have 0 painted faces?

(n - 2)^3, the fully internal cubes with no exposure to the surface.

What is the fundamental property of a standard die used in Dice problems?

Opposite faces of a standard die always sum to 7 (1-6, 2-5, 3-4).

In Dice reasoning, what is the difference between 'standard' and 'ordinary' (non-standard) dice rules?

In a standard die opposite faces sum to 7; for any die, if two different positions show four common faces, the two remaining (odd) faces are opposite to each other.

State the dice rule for finding opposite faces from two views showing one common face.

If one face is common (same) in two different views of a die, then the remaining faces rotate in order; the faces that never appear adjacent across the views are opposite to each other.

When two dice views share a common pair of adjacent faces, how do you find the face opposite a given face?

Identify which faces are shown adjacent to the given face in both views; the face that is never shown adjacent to it is the one opposite to it.