Select the option figure in which the given figure is embedded (rotation is…

Concept. An embedded-figure item asks whether one drawing sits inside another as an exact sub-drawing. Because rotation is barred, the hidden figure must appear at the same orientation and at the same size: every one of its strokes has to lie along a straight line that the larger drawing already contains, and every angle between those strokes has to survive unchanged. The dependable method is therefore not to stare at the pictures, but to reduce the given figure to a short list of strokes — their directions, their lengths and the points at which they meet — and then to look for one place in a candidate drawing where all of those directions coexist in exactly that arrangement.

Application. Reduce the given figure to its strokes:

1. One long horizontal stroke.

2. One long vertical stroke that cuts the horizontal, reaching a short way above it and running well below it.

3. A stroke rising at about 45° from the horizontal on the left up to the top end of the vertical; together with the horizontal it closes an upward-pointing triangle whose apex sits on the vertical.

4. From that same apex, a single straight stroke falling at about 45° to the right; it crosses the horizontal and carries on to a point below it.

5. A stroke rising at about 45° from that lower point back to the horizontal, closing a small downward-pointing triangle that hangs below the horizontal on the right of the vertical.

So the arrangement to hunt for is: a horizontal and a vertical that genuinely cross; one pair of 45° lines meeting on the vertical a short way above that crossing, forming a right-angled apex; and a second, smaller pair of 45° lines meeting below the horizontal, offset to the right by roughly one and a half times the height of the first triangle.

Cross-check. Exactly one of the four drawings supplies that package — the one ruled into three vertical bands and three horizontal bands. Its central vertical rule and its lower horizontal rule cross each other; the square’s two corner-to-corner diagonals cross on that vertical rule a short way above the horizontal rule, which is precisely the upward-pointing triangle with its apex on the vertical; and the falling diagonal carries on below the horizontal rule until it meets another long slant, closing the small downward-pointing triangle to the right. Set the given figure down with its own horizontal-vertical crossing on that lattice intersection and all five of its strokes land on lines that are already drawn, at the same size and with no turning.

Running the same test on the remaining drawings stops each of them at the very first stroke:

• Those whose only full-width lines are the frame’s own top and bottom edges carry no interior horizontal at all, so the crossing demanded by strokes 1 and 2 cannot be built anywhere inside them.

• The one that does carry a single interior full-width line has its two corner diagonals meeting below that line rather than above it, so the upward-pointing triangle of strokes 3 and 4 cannot be seated with its apex on a vertical above the horizontal.

Hence the figure ruled into a three-by-three lattice, whose corner-to-corner diagonals cross on its central vertical rule, is the one in which the given figure is embedded.