Chapter 25
Embedded Figures
Find the small figure inside the busy one: pick the anchor, drop the options, trace the lines.
Embedded Figure questions ask you to find a small figure hidden inside a larger, busier one. There is nothing to calculate and nothing to memorise. You only have to look in the right way. The question gives you one figure and four answer figures, and you decide which answer figure has the given figure traced inside it, line for line.
The chapter has four types, arranged in the order in which they are worth learning:
- Type 1. Target hidden in one of four options. The standard question: the small figure comes first and you pick the option that contains it. The version in which rotation is allowed is part of this type.
- Type 2. Option hidden in the question figure. The big figure comes first and the options are small. The 'which one is NOT present' version is part of this type.
- Type 3. Near-identical options. The four options look like copies of each other and differ by one segment.
- Type 4. Stacked or repeated pair [New Pattern]. The target holds two copies of a shape in a fixed arrangement.
Most students find these questions slow because they scan every option from corner to corner. Here you will build a faster habit: pick the one unusual feature of the small figure, the anchor, search for only that, drop the options that do not have it, and trace the rest. Embedded figures appear often in the non-verbal part of SSC and Railway papers, though not in every shift, and they are among the quickest marks when you work by elimination. Counting questions such as 'how many triangles' belong to a separate chapter, Counting Figures.
What is an embedded figure?
A figure is embedded (hidden) in a bigger figure when you can place the small figure on the big one so that every line of the small figure lies exactly on a line of the big figure. Same size, same shape, same direction.
| Term | Meaning |
|---|---|
| Target | The small figure you must find |
| Host | The bigger, busier figure that may contain it |
| Anchor | The most unusual part of the target: a sharp angle, a long slanting line, a T-junction |
| Trace | Following the target line by line inside the host |
[[fig:0]]
In the picture the target is a Z. In the host it is not drawn separately. It is made from three lines that already belong to the host, and the lines around it do not matter. Extra lines in the host are allowed. Missing lines are not.
Three conventions: no turning, no flipping, same size
Unless the question says otherwise, three conventions hold in every embedded-figure question.
- No rotation. The target must appear in the same direction as drawn. A turned copy is a different figure.
- No flipping. A mirror copy (S for Z) is a different figure, even when rotation is allowed.
- Same size. The target cannot be enlarged or shrunk. A smaller Z is not the Z.
[[fig:0]]
Look at the four figures. Only the first is the target. The second is its mirror image, the third is the same Z turned through a quarter turn, and the fourth is a smaller copy. At first glance they feel alike, and that is exactly why paper setters use them as wrong options.
Two more points. The target must be complete: if one line is missing, or a straight line is bent in the host, the option is wrong. And the lines must meet at the same angles. Always read the question: if rotation is allowed, the question says so.
Anchor, eliminate, trace
Searching every option line by line wastes time. Use three moves instead.
1. Anchor. Look at the target and pick its rarest part: a slanting line, an acute angle, a T-junction, a short stub. Ordinary parts, such as a plain corner, can be found anywhere, so they make poor anchors.
2. Eliminate. Scan each option for the anchor, in the same direction and the same size. If it is not there, cross the option out at once.
3. Trace. For the options that survive, trace the whole target line by line. One missing line or one wrong length rejects the option.
[[fig:0]]
In the picture the anchor of the Z is its slanting line, shown in orange. The mirror option and the steeper option fail at the anchor itself. The option with the short top line passes the anchor but fails at the trace. Only the last option passes everything. Anchor, eliminate, trace.
Type 1
Target hidden in one of four options (rotation not allowed / allowed)
In this question the small figure is shown first, and four busy figures follow it. In one of them the small figure can be traced, line for line. Before you look at a single option, read the bracket at the end of the question. It fixes the conditions: 'rotation is not allowed' means the target must appear in the same direction as drawn; 'rotation is allowed' means it may be turned, but never flipped.
Do not stare at the options hoping the answer will jump out. Work in order. First choose the anchor of the target, its rarest part. Then look for that part in each option, in the same direction. An option without it is gone. Finally, trace the whole target in the options that remain.
[[fig:0]]
In the figure the target is a diamond with a short line from its right corner and a cross-bar at the end of that line. The anchor is the cross-bar standing on the end of the line: a T-junction on the right of a diamond. The traced lines are shown in red.
Two things make wrong options look right. The first is a mirror copy: the same figure with the tail on the left. The second is a turned copy: the tail pointing up or down. Both use the same lines placed differently, and both are rejected here.
[[fig:1]]
The target must be present in the same direction, at the same size, and complete.
When rotation is allowed. The target may be turned, mostly by quarter turns, so the search changes from 'same direction' to 'same junctions and lengths'. The size and the ban on flipping stay exactly as before. A turned F is still an F. A mirror F is not.
[[fig:2]]
Because direction is free, do not describe the target by direction ('the line goes up'). Describe it by its junctions and lengths: 'a line of 3, with an arm of 2 at one end and a short arm of 1 standing one step from that end, both on the same side'. Then search for that description in any direction.
[[fig:3]]
A T stays a T when turned: a line that ends in the middle of another line. Describe the target by its junctions and lengths, not by its directions.
To catch a mirror copy, use the left-hand test. Stand at the end of the long line where the arms are, and look along the line. In F the arms fall on your left hand. If in the host they fall on your right hand, the figure is a mirror copy and is rejected, however you turn it.
If the target is symmetric, such as a T, a plus or a square, its mirror image is the same figure, so the left-hand test is not needed.
- Select the option figure in which the given figure (X) is embedded as its part (rotation is NOT allowed).
- Select the option figure in which the given figure (X) is embedded as its part (rotation is NOT allowed).
- Select the option figure in which the given figure (X) is embedded as its part (rotation is NOT allowed).
- Select the option figure in which the given figure (X) is embedded as its part (rotation is NOT allowed).
- Select the option figure in which the given figure (X) is embedded as its part (rotation is NOT allowed).
Type 2
Option hidden in the question figure (including 'NOT present')
Here the roles are reversed. The big figure is given first and the four options are small. You must find which option can be traced inside the big figure (or, in the 'NOT' version, which one cannot). The host is the same for all four options, so do the hard work only once: read the host and list its lines with their directions.
List what the host offers: the outer square, the diamond, the midlines, the diagonals. Then take the options one by one and test each side. An option is present only if every side lies along a line of the host and has the right length. Stop at the first side that is missing.
[[fig:0]]
The option does not have to sit where it is drawn. It may be found anywhere in the host, as long as it has the same direction and the same size. In the picture, the red parallelogram uses four lines of the host: the bottom edge, one side of the diamond, the midline and the diagonal.
A side may be part of a longer line: a side of 3 can lie on a line of 6. But a side cannot be bent, and it cannot be longer than the line that carries it.
[[fig:1]]
The second picture shows the common failure. A small square of half the side needs a vertical line through the middle, shown dashed in red. The host does not have it. One missing line is enough to reject an option. List the lines of the host first; then each option is a quick yes or no.
The 'NOT present' version. Three options are in the host and one is not. The method is the same with the aim reversed: for each option, test its unusual side, the side least likely to be in the host, and stop at the first line that is absent. That option is the answer. Read the word NOT twice; this is where careless marks are lost.
[[fig:2]]
In the figure the host is a square with a diagonal and a horizontal midline. Three options are ticked. The small square is crossed, because it needs a vertical line through the middle, and the host has none. Test the unusual side first; the first missing line decides.
If two options both look doubtful, compare them directly. The absent option usually has one side that the other does not, and that side is the suspect. Also remember the option may be found anywhere in the host, not only where it is drawn, so before you call an option absent, check the other places it could sit.
Type 3
Near-identical options
In this type the four options look almost the same. They are built from the same lines, and they differ by a single segment: a line that is bent instead of straight, a line that is short instead of long, a gap in a line, or a line in the wrong place. The target decides which option has the right segment.
Do not compare each option with the target from scratch. First compare the options with each other and find where they differ. Then test only that segment against the target.
[[fig:0]]
In the figure the target is a cup: a base of 3, a left arm of 1 and a right arm of 2. The four options share a base, two arms and a bar on top. In the first, the right arm is only 1 long. In the third, the base has a gap. In the fourth, the right arm is again only 1 long, because the arms are swapped in length. Only the second has an unbroken base and a right arm of 2. The differing segment is marked in red.
These small differences are the usual tricks of the paper setter: straight versus bent, short versus long, joined versus a gap. Remember that a line longer than needed is fine, because extra length can be ignored, but a line shorter than needed is not. Find the one segment that differs, and test only that.
Type 4
Stacked or repeated pair [New Pattern]
New-pattern questions give a target that contains two or more copies of the same shape in a fixed arrangement: for example two squares one above the other with a gap, or two triangles in the same direction. For an option to contain the target, it must show all the copies, each complete, with the same spacing and the same arrangement. Finding one copy is not enough.
Work in two steps. First find one copy using the usual anchor method. Then check that the second copy sits exactly where the target says: the same direction, the same distance and the same side.
[[fig:0]]
In the figure the target has two squares with a gap equal to one square. In the host, the red squares are the pair. The square in the middle is an extra, and extra lines do not matter.
[[fig:1]]
The wrong options are easy to make. Two squares that touch have no gap. Two squares side by side change the arrangement. Squares with a bigger gap change the spacing. One copy is not enough; both copies and the spacing must match.
When the copies are lined up on a common line, the line itself may run through the gap, and that is fine. What counts is that the copies are present in the right places.