13.2 Linear Sequencing, Ranking & Slot-Based Puzzles
Key Takeaways
- Linear sequencing puzzles require ordering N distinct entities across 1D sequential slots based on explicit spatial, temporal, or ordinal relationships.
- Block building rules combine adjacent entities into single multi-entity units, reducing the effective number of movable items on the board.
- Relative placement chains (A...B...C) establish directional flow across slots, instantly creating boundary deductions for extreme slots.
- The Split-Board (Case Analysis) strategy involves creating 2 or 3 parallel master diagrams whenever a key rule limits a critical entity to a small number of mutually exclusive positions.
- Systematic identification of dead slots (positions where an entity or block cannot fit due to boundary or spacing constraints) narrows down valid arrangements instantly.
Last updated: August 2026
Linear Sequencing, Ranking & Slot-Based Puzzles
Linear Sequencing Puzzles—frequently referred to as 1D ordering games—constitute the single most common category of analytical reasoning questions on the NTS GAT General. These games present a scenario where $N$ distinct entities must be arranged in a strict linear sequence across $N$ numbered slots (such as slots 1 through 6, Monday through Saturday, or presentation order 1st through 5th). Mastering linear sequencing requires a deep understanding of block dynamics, relative spacing, boundary conditions, and case analysis.
Principles of 1D Linear Ordering Games
In a standard 1D linear sequencing puzzle, the slots possess an inherent directional order. Always establish a clear, left-to-right visual baseline on your scratchpaper:
\hline \text{Slot 1} & \text{Slot 2} & \text{Slot 3} & \text{Slot 4} & \text{Slot 5} & \text{Slot 6} \\ \hline \text{Earliest / First} & \dots & \dots & \dots & \dots & \text{Latest / Last} \\ \hline \end{array}$$ ### Key Ordering Terminology - **"Immediately before / directly preceding"**: Indicates strict adjacency ($[AB]$). $A$ is in slot $k$ and $B$ is in slot $k+1$. - **"Sometime before / earlier than"**: Indicates relative ordering ($A \dots B$). $A$ occupies a slot with a lower number than $B$, but they are not necessarily adjacent. - **"Exactly $X$ slots separate A and B"**: Indicates a fixed gap block with $X$ empty slots between $A$ and $B$ ($[A \; \underbrace{\text{\underline{ \;\;\;\; }}}_X \; B]$). For example, "Exactly two slots separate A and B" means $|\text{Slot}_A - \text{Slot}_B| = 3$ (e.g., slots 1 and 4). --- ## Rule Structures & Block Building Techniques ### 1. Block Building When a rule states that two or more entities must be placed consecutively (e.g., "Entity Q presents immediately before Entity R"), combine them into a single structural block: **$[QR]$**. Treating $[QR]$ as a single compound entity reduces the total number of items to arrange from $N$ to $N-1$, simplifying board management. If the rule does not specify order (e.g., "Q and R present in consecutive slots"), represent the block as **$[Q, R]$** with a bidirectional arrow indicating that the block can be either $[QR]$ or $[RQ]$. ### 2. Spacing Blocks & Dead Slots Spacing rules restrict where blocks can fit on the board. For example, if a block $[QR]$ requires 2 adjacent slots, and slot 5 is already occupied by another entity, $[QR]$ cannot start in slot 5. Furthermore, if $[QR]$ requires slot 6, it cannot start in slot 6 because $R$ would spill past the boundary of a 6-slot board. Slot 6 is a **dead slot** for the start of block $[QR]$. ### 3. Relative Placement Chains Combine multiple relative ordering rules into a single linear chain. If Rule 1 states $S \dots T$ and Rule 2 states $T \dots U$, merge them into the master chain: $$S \dots T \dots U$$ This chain immediately yields powerful boundary deductions: - $S$ cannot be in the last two slots (slots 5 or 6 on a 6-slot board). - $U$ cannot be in the first two slots (slots 1 or 2). - $T$ cannot be in slot 1 or slot 6. --- ## The Split-Board (Case Analysis) Strategy The **Split-Board** strategy is the most powerful advanced technique for solving linear games. Whenever a rule limits a key entity or block to exactly **two or three mutually exclusive possibilities**, stop trying to hold multiple scenarios in your head. Instead, split your scratchpaper master board into parallel sub-diagrams (Case 1 and Case 2). ### Common Split Triggers - An entity is restricted to extreme boundary slots (e.g., "Entity P must be in Slot 1 or Slot 6"). - A large block can only fit in two specific positions on the board. - A conditional rule splits the game into two clear paths based on whether a key entity is included or excluded. --- ## Complete Step-by-Step Worked NTS Setup & Question Set To see linear sequencing in action, examine the following complete worked NTS game setup and deduction workflow. ### Game Setup Scenario Six job candidates—**P, Q, R, S, T, and U**—are scheduled for individual job interviews across six consecutive time slots numbered **1 through 6**. Exactly one candidate is interviewed in each slot, subject to the following rules: 1. Candidate **P** must be interviewed in **Slot 1** or **Slot 6**. 2. Candidate **Q** must be interviewed immediately before Candidate **R** ($[QR]$). 3. Candidate **S** must be interviewed earlier than Candidate **T** ($S \dots T$). 4. Candidate **U** cannot be interviewed in **Slot 5** ($U \neq 5$). 5. Exactly **two** interview slots separate Candidate **P** and Candidate **R**. --- ### Master Deduction Breakdown Let's apply the **Split-Board** strategy based on Rule 1 ($P = 1 \lor 6$). #### Case 1: Candidate P is placed in Slot 1 ($P = 1$) - By Rule 5, exactly two slots separate $P$ and $R$. Since $P = 1$, $R$ must be placed in **Slot 4** ($[P \; \underline{\text{2}} \; \underline{\text{3}} \; R]$). - By Rule 2, $Q$ must be interviewed immediately before $R$. Since $R = 4$, $Q$ must be in **Slot 3** ($[Q R] \rightarrow \text{Slots } 3, 4$). - The remaining open slots in Case 1 are **Slot 2**, **Slot 5**, and **Slot 6** for entities **{S, T, U}**. - By Rule 4, $U \neq 5$. Therefore, $U$ must be placed in either Slot 2 or Slot 6. - By Rule 3, $S$ must appear before $T$ ($S \dots T$). $$\text{Case 1 Master Board: } \begin{array}{|c|c|c|c|c|c|} \hline \text{Slot 1} & \text{Slot 2} & \text{Slot 3} & \text{Slot 4} & \text{Slot 5} & \text{Slot 6} \\ \hline \mathbf{P} & \text{S / U} & \mathbf{Q} & \mathbf{R} & \text{S / T} & \text{T / U} \\ \hline \end{array}$$ #### Case 2: Candidate P is placed in Slot 6 ($P = 6$) - By Rule 5, exactly two slots separate $P$ and $R$. Since $P = 6$, $R$ must be placed in **Slot 3** ($[R \; \underline{\text{4}} \; \underline{\text{5}} \; P]$). - By Rule 2, $Q$ must be interviewed immediately before $R$. Since $R = 3$, $Q$ must be in **Slot 2** ($[Q R] \rightarrow \text{Slots } 2, 3$). - The remaining open slots in Case 2 are **Slot 1**, **Slot 4**, and **Slot 5** for entities **{S, T, U}**. - By Rule 3, $S \dots T$. Thus $S$ must be in Slot 1 or Slot 4, and $T$ must be in Slot 4 or Slot 5. - By Rule 4, $U \neq 5$. This forces $U$ into Slot 1 or Slot 4. $$\text{Case 2 Master Board: } \begin{array}{|c|c|c|c|c|c|} \hline \text{Slot 1} & \text{Slot 2} & \text{Slot 3} & \text{Slot 4} & \text{Slot 5} & \text{Slot 6} \\ \hline \text{S / U} & \mathbf{Q} & \mathbf{R} & \text{S / T / U} & \mathbf{T} & \mathbf{P} \\ \hline \end{array}$$ *Crucial Inference in Case 2:* In Case 2, since $U \neq 5$ and $S \dots T$, Candidate **T** is forced into **Slot 5** if $U$ takes Slot 4 and $S$ takes Slot 1! --- ### Practice Question Walkthroughs #### Question 1: If Candidate P is interviewed in Slot 1, and Candidate U is interviewed in Slot 2, which candidate must be interviewed in Slot 5? - **Analysis**: Refer to Case 1 ($P = 1$). If $U = 2$, then the remaining entities for Slots 5 and 6 are $S$ and $T$. Since Rule 3 dictates $S \dots T$, $S$ must be placed in **Slot 5** and $T$ must be placed in **Slot 6**. Therefore, Candidate $S$ MUST be interviewed in Slot 5. #### Question 2: Which of the following is a complete and accurate list of candidates who COULD be interviewed in Slot 1? - **Analysis**: Looking across both master cases: In Case 1, $P$ is in Slot 1. In Case 2, either $S$ or $U$ can occupy Slot 1 (since $S \dots T$ permits $S = 1$, and $U \neq 5$ permits $U = 1$). Thus, the candidates who could be in Slot 1 are **P, S, and U**.Loading diagram...
Test Your Knowledge
In a 6-slot linear sequence game (slots 1 to 6), if Entity Q must be placed immediately before Entity R ([QR]), and Entity R is assigned to Slot 4, which slot MUST Entity Q occupy?
A
B
C
D
Test Your Knowledge
Based on the worked interview setup (entities P, Q, R, S, T, U across slots 1 to 6), if Candidate P is interviewed in Slot 1, which slot MUST Candidate R occupy?
A
B
C
D
Test Your Knowledge
What is the main structural trigger for deploying the Split-Board (Case Analysis) strategy during an NTS linear sequencing puzzle?
A
B
C
D
Test Your Knowledge
In a 6-candidate ordering game where Candidate S must be interviewed before Candidate T (S ... T), if Candidate S is placed in Slot 4, which slots are legally available for Candidate T?
A
B
C
D