Master letter and word puzzles, dice face rules, number matrix patterns, triangle and rectangle counting formulas, route map calculations, and coded operations with structured notes and timed practice inside the Learn at My Place competitive flow.
Reserved leaderboard placement in the competitive reasoning notes layout.
Puzzles in CUET UG span eight distinct sub-types — from counting letters in words to decoding artificial operators. Each sub-type has a specific technique that makes it fast and reliable when practised systematically.
The common thread across all puzzle types is that a brief setup step — labelling positions, writing a formula, drawing a route — converts a confusing question into a mechanical calculation. That setup habit is what separates fast solvers from slow ones on exam day.
Natural break after high-intent concept reading.
These questions ask you to count specific letters in a word, or rearrange a word after interchanging two specified letters and then identify the new word from options.
After the swap, read the result left to right to find the new word. Never swap mentally — position errors are the most common mistake in this sub-type.
Standard dice have three fixed opposite pairs: 1↔6, 2↔5, 3↔4. In any single position of a die you can see at most three faces. The face on the bottom is always the opposite of the top.
Use this rule to eliminate impossible pairings and narrow the opposite to the only remaining face. In adjacent-face questions, any face that is visible alongside a given face is definitely not its opposite.
A 3×3 or 3×4 matrix has a hidden rule that links numbers across each row, column, or diagonal. Your task is to find the missing number that satisfies the same rule.
For a 3×3 matrix, a common pattern is that the middle cell equals the sum (or product) of the surrounding cells divided by a constant. Verify the rule on the two complete rows or columns before applying it to the incomplete one.
A letter series puzzle gives a sequence with one or more blanks and asks you to fill in the missing letters. The key is to detect the repeating block or the arithmetic step in the position values.
If the differences repeat — for example +3, +3, +3 — the pattern is arithmetic. If they alternate — +2, +5, +2, +5 — the series has two interleaved sub-series. Identify which sub-series contains the blank and solve only that strand.
Counting triangles in a figure is systematic when you label all vertices and then list triangles by size: unit triangles first, then two-unit combinations, then the largest triangles.
For irregular figures, label all intersection points alphabetically and list every set of three points that forms a triangle without any internal line passing through it. Crossing off listed sets prevents double-counting.
In an m×n grid (m horizontal lines, n vertical lines), rectangles are formed by choosing 2 of the m horizontal lines and 2 of the n vertical lines.
For a 4×4 grid of unit squares (5 horizontal and 5 vertical lines): 5C2 × 5C2 = 10 × 10 = 100. Squares are a subset of rectangles; do not subtract them unless the question specifically asks for non-square rectangles.
Route map questions give a traveller's journey in segments — direction, distance, and sometimes speed — and ask for total distance, final displacement, or average speed over the full journey.
Draw the route on a rough coordinate grid. Use compass directions: North is +y, East is +x. Add each segment as a vector. The final position minus the starting position gives displacement. Use Pythagoras when the final path is not along a single axis.
In these questions, a new operator (often a symbol like ★ or #) is defined through one or two examples. You must reverse-engineer the definition and then apply it to the actual question.
Test your decoded rule on any second example provided. If it matches, your rule is correct. Common patterns hide a combination of two ordinary operations, for example a★b = (a + b) × (a − b) = a² − b². Verify before applying.
Write out T-R-I-A-N-G-L-E and compare each letter to the one immediately after it.
T(20) > R(18): No. R(18) > I(9): No. I(9) > A(1): No. A(1) < N(14): Yes. N(14) > G(7): No. G(7) > L(12): Yes. L(12) > E(5): No.
Count: 2 letters are followed by a later-alphabet letter.
Standard dice rule gives 1↔6, 2↔5, 3↔4.
So the face opposite to 3 is 4.
The common face in both positions is 1 (top).
By the two-position rule, since 2 and 3 are both adjacent to 1 in different positions, 2 and 3 are adjacent to each other.
2 is therefore not opposite to 1 (common face). The only face not yet placed opposite 2 must be found by elimination: 1 is common, 3 is adjacent. The opposite of 2 is 5.
Check the row rule: each row's third element equals the sum of the first two.
Row 1: 2+3=5 ✓. Row 2: 4+6=10 ✓. Row 3: 6+?=15, so ?=9.
Convert to positions: A=1, D=4, G=7, J=10, __, P=16.
Difference between consecutive terms: +3 each time.
After J(10): 10+3=13 = M.
Use the formula for n=4 rows: n(n+2)(2n+1)/8 = 4×6×9/8 = 216/8 = 27.
This counts all upward-pointing and downward-pointing triangles of every size.
A 3×4 grid of unit squares has 4 horizontal lines and 5 vertical lines.
Total rectangles = ⁴C₂ × ⁵C₂ = 6 × 10 = 60.
Draw the path: 5 km North (+y) and 12 km East (+x).
Displacement = √(5² + 12²) = √(25+144) = √169 = 13 km.
Time for first leg: 60/30 = 2 hours. Time for second leg: 60/60 = 1 hour.
Total distance = 120 km. Total time = 3 hours.
Average speed = 120 ÷ 3 = 40 km/h.
Test the pattern: 3+5=8, but 8×2=16 ✓. Check: 4+6=10, 10×2=20 ✓.
Rule: a ★ b = (a+b) × 2.
7 ★ 9 = (7+9) × 2 = 16 × 2 = 32.
Use the sectional practice page to work through each puzzle sub-type in isolation — dice, matrix, counting figures, route maps, and coded operations. Then take the full mixed mock to build exam-speed across all eight types together.
Move straight from chapter-wise questions into a subject test, then loop back into weaker areas instead of ending the session here.