📚 Delhi TET – Reasoning Ability (Puzzles)
Advanced, MIT‑style study notes
(From first principles → rigorous reasoning → deeper theory → edge cases → challenging practice problem)
1. Why Puzzles?
| Aspect | Why it matters for TET | Example |
|---|---|---|
| Cognitive flexibility | Detects how quickly you can switch between different problem types | Sequence vs. logic puzzle |
| Pattern recognition | Tests ability to spot subtle regularities under time pressure | Identifying the next number in a series |
| Deductive reasoning | Checks systematic elimination and “proof by contradiction” | “Only one person can be the teacher” puzzle |
| Speed & accuracy | Exam requires 30‑45 min for 40‑50 questions | 1 min per puzzle on average |
2. Puzzle Taxonomy (Delhi TET)
| Category | Sub‑type | Typical Constraints | Example |
|---|---|---|---|
| Number Puzzles | Sequences, series, “find the missing number” | Arithmetic/Geometric, Fibonacci, alternating, pattern‑based | 2, 5, 10, 17, … |
| Logic/Grid Puzzles | 4‑x‑4, 5‑x‑5, 6‑x‑6 “who lives where” | One‑of‑each, “exactly one” rules | 5 houses, 5 nationalities, 5 drinks |
| Word/Letter Puzzles | Anagrams, word ladders, letter‑placement | Word length, letter frequency | “Arrange letters to form a word” |
| Spatial Puzzles | 2‑D/3‑D arrangements, “placing tiles” | Orientation, adjacency | “Place 6 blocks to cover a board” |
| Set‑Theory/Boolean Puzzles | Inclusion, intersection, union | Logical operators, truth tables | “If A then B; not C” |
| Combinatorial Puzzles | Permutations, combinations, counting | Exclusion, “at least” | “How many ways to seat 5 people? 5! = 120” |
Tip – In the exam, puzzles are self‑contained: all necessary information is given in one statement, so you can treat each as a small world.
3. First Principles: Modeling a Puzzle
Goal – Translate words into mathematical constraints that can be solved by deduction or brute‑force search.
3.1. Variables
| Symbol | Meaning | Example |
|---|---|---|
| (x_i) | Decision variable (binary, integer, categorical) | (x_1 = 1) if John is Teacher, else 0 |
| (\mathbf{X}) | Vector of related variables | ((x_1, x_2, …, x_n)) |
| (S) | Set of possible values | (S = {1,2,3,4,5}) |
3.2. Constraints
| Type | Formalism | Example |
|---|---|---|
| Equality | (x_i = c) | (x_1 = 3) |
| Inequality | (x_i \neq x_j) | No two houses share the same colour |
| Logical | (x_i \Rightarrow x_j) | If John is a teacher, then Mary is a student |
| Arithmetic | (x_i + x_j = k) | Sum of door numbers = 15 |
| Set | (x_i \in S) | Color ∈ {Red, Green, Blue} |
3.3. Modeling Approaches
| Approach | When to use | Tool/Method |
|---|---|---|
| CSP (Constraint Satisfaction Problem) | Discrete variables, relational constraints | Backtracking, forward checking |
| SAT (Boolean Satisfiability) | Binary variables, logical constraints | SAT solver, DPLL algorithm |
| ILP (Integer Linear Programming) | Linear constraints, optimization | Simplex + branch‑and‑bound |
| Graph Theory | Adjacency or connectivity | Graph coloring, bipartite matching |
Rule of Thumb – For TET puzzles, CSP + backtracking is enough; you rarely need advanced solvers, but understanding the underlying theory helps avoid pitfalls.
4. Systematic Solving Process
| Step | What to Do | Why It Helps |
|---|---|---|
| 1. Parse the statement | Identify all entities (people, houses, numbers) and attributes (color, drink, age). | Prevents missing a hidden constraint. |
| 2. List variables | Assign a variable to each attribute of each entity. | Gives a clear map to fill in. |
| 3. Draw a grid (if needed) | Use a 2‑D table: rows = entities, columns = attributes. | Visual representation clarifies relationships. |
| 4. Encode constraints | Write each clue as a formal |