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Shape Assembly

4 questions

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Question 1Question →

A horizontal sliding base is open on the right side. The floor of this base has a small square depression located at the far left end. Three flat shapes must be slid horizontally into the base from the right side to completely fill the empty space.

Shape M: A small square that perfectly fits into the left-side depression.
Shape N: A flat rectangular plate that rests on the floor of the base, covering the left half (including the depression).
Shape P: A large rectangular block that seals the right half of the base.

Arrange the shapes in the correct chronological order they must be inserted from the right side to ensure all pieces can reach their intended final positions without blocking each other.

Drag items to arrange them in the correct order

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Answer

The correct order of assembly is: Shape M, then Shape N, then Shape P.
Shape M must enter first because it goes the furthest in (into the depression). Shape N follows to sit above the depression, and Shape P goes last to seal the entrance. Any other order results in physical collisions.

Step-by-Step Solution

1
Identify the piece that must be placed deepest into the base.
Shape M is the only piece that fits in the left-side depression.
If other pieces are placed first, they will block the path to the depression.
2
Determine the next piece that must slide in without being blocked.
Shape N must go next to cover the floor and sit on top of the depression.
Shape P seals the right half, so it would block Shape N if inserted second.
3
Place the final piece to complete the assembly.
Shape P is inserted last.
It perfectly seals the right opening of the base, finishing the structure.

Key Concept

Translation-based assembly sequence and collision avoidance
Estimated Time:45s
Question 2Question →

Three geometric puzzle pieces must be assembled in a specific sequence based on their physical connection points. Piece A has a single protruding tab. Piece B has a slot that exactly fits Piece A's tab, and a peg on its opposite side. Piece C has a circular hole that fits Piece B's peg. Arrange the following assembly steps in the logically required physical sequence, starting with Piece A as the foundation.

Drag items to arrange them in the correct order

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Answer

The correct logical sequence is to place Piece A first, attach Piece B to Piece A, align Piece C over Piece B, and finally press Piece C into place.
The assembly must strictly follow the physical constraints of the connection points. Piece A provides the initial tab. Piece B must connect to Piece A's tab to integrate properly, which then positions its peg. Piece C must then connect to Piece B's peg. Attempting any other order physically fails because the necessary connection points would not be available.

Step-by-Step Solution

1
Identify the foundation piece.
Piece A is placed first as the base.
The prompt establishes Piece A as the starting component.
2
Determine the next piece that physically connects to Piece A.
Piece B is attached to Piece A.
Piece B has the slot that fits Piece A's tab, making it the only valid next step.
3
Determine the piece that connects to the newly exposed peg on Piece B.
Piece C is aligned with Piece B.
Piece C has the hole that fits Piece B's peg.
4
Finalize the overall assembly.
Piece C is pressed onto Piece B.
This physical action completes the integration of all three components.

Key Concept

Multi-Component Integration
Question 3Question →

Match each left-side puzzle component (1-4) with its exact complementary right-side component (A-D) that will interlock seamlessly to form a perfect solid rectangle. The mating edges are vertical and their profiles are described sequentially from top to bottom.

Click a left item, then click its matching right item

Items

Component 1: Right boundary features a triangular notch, a straight vertical segment, and a small semi-circular tab.
Component 2: Right boundary features two consecutive sharp zigzag tabs, followed by a square notch.
Component 3: Right boundary features a large semi-circular recess, a straight vertical segment, and a 45-degree angled tab.
Component 4: Right boundary features a wide rectangular tab, a narrow rectangular tab, and a wide rectangular recess.

Matches

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Answer

Component 1 pairs with Component C; Component 2 pairs with Component D; Component 3 pairs with Component A; Component 4 pairs with Component B.
For two irregular pieces to form a seamless rectangle without rotation, the mating edge of the right piece must be the exact spatial inverse of the left piece's mating edge. Every protrusion on the left component must meet a corresponding recess of identical shape, size, and location on the right component, and vice versa.

Step-by-Step Solution

1
Analyze the edge profile of Component 1 from top to bottom.
Identified a sequence of a triangular notch, a flat segment, and a small semi-circular tab.
Establishing the sequence of features is required to find the exact inverse complement.
2
Search the right-side components for the inverse of Component 1's profile.
Component C provides the exact inverse: a triangular tab (to fill the notch), a flat segment, and a small semi-circular notch (to receive the tab).
A seamless fit requires every recess to have a corresponding protrusion of the exact same shape and size.
3
Analyze Component 2 and locate its inverse.
Component 2 has zigzag tabs and a square notch; Component D has the matching zigzag notches and a square tab.
Matching the sharp angular features precisely ensures the geometry locks together correctly without collisions.
4
Analyze Component 3 and locate its inverse.
Component 3 has a large semi-circular recess and angled tab; Component A has the matching large semi-circular tab and angled notch.
The large curved feature and angular tab pair uniquely with their exact inverse.
5
Confirm the remaining pair (Component 4 and Component B).
Component 4's sequence of wide/narrow tabs and wide recess perfectly complements Component B's wide/narrow recesses and wide tab.
Verifying the final pairing ensures no sequence matching errors were made in previous steps.

Key Concept

Identifying complementary inverse shapes for irregular edge assembly.

Alternative Method

Mentally draw the 'negative space' along the right edge of each left-side component. This imaginary shape represents the exact profile you must search for among the right-side components.
Estimated Time:1m 30s
Question 4Question →

During industrial fabrication, specific metal plates must be welded together to form solid, continuous surfaces without gaps. Match each left-side metal plate, characterized by its specialized right-side welding seam, with the appropriate right-side plate that possesses the exact complementary left-side seam.

Click a left item, then click its matching right item

Items

Protruding dovetail joint
Inward semi-cylindrical channel
Protruding jagged sawtooth profile
Inward square-cut keyway

Matches

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Answer

The protruding dovetail joint matches the inward dovetail socket; the inward semi-cylindrical channel matches the protruding semi-cylindrical rod; the protruding sawtooth profile matches the inward sawtooth recess; and the inward square-cut keyway matches the protruding square-cut key.
A flawless weld between two plates requires that every extending structural feature (positive space) on one plate is exactly accommodated by a corresponding cut-out (negative space) of the identical geometry on the adjoining plate, allowing them to slide together without rotation.

Step-by-Step Solution

1
Examine the right-edge welding seam of each left-side plate to determine if it is a protrusion (positive space) or a recess (negative space).
Identified two protrusions (dovetail, sawtooth) and two recesses (channel, keyway).
Understanding the physical geometry is the first step to finding a complementary fit.
2
Search the right-side plates for the exact inverse geometric shape for each specific profile.
Paired the dovetail protrusion with the dovetail socket, and the sawtooth protrusion with the sawtooth recess.
A protrusion requires an identical recess to form a flush surface.
3
Match the remaining recessed left-side plates with their corresponding protruding right-side plates.
Paired the semi-cylindrical channel with the rod, and the square-cut keyway with the key.
A recess must be filled by an identical protrusion to eliminate gaps.

Key Concept

Identifying complementary positive and negative spatial geometries (protrusions and recesses) to seamlessly interlock irregular edges.
Estimated Time:45s
Shape Assembly Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin