Puzzles

Module 04 — Lesson 0004 · In Depth · 50 min

Two puzzle families: visual numbers (find the hidden operation in a shape) and analytical arrangements (place people by constraints). One tests magnitude sense; the other tests positional logic.

Part A: Visual Number Puzzles

Numbers in shapes (matrices, triangles, circles, trees) follow a hidden operation. Find it on a complete set, verify on a second, then apply to the missing one.

1. Matrix and Grid Puzzles (Rows × Columns)

Relationship is row-wise or column-wise — test both directions.

Arithmetic: last in row/col = sum/difference/product of previous. Example: Row3 = Row1 + Row2.
Squares/cubes: one cell is square/root of another. Formulas: C = √(A+B) or C = A² − B²
Combined: Z = (X × Y) + k (constant k across rows/cols)

Test row-wise first (sum), then column-wise. Rule must hold for at least two complete rows/cols before applying to missing cell.

2. Triangular and Polygon Puzzles

Numbers at vertices A,B,C, center X is the resultant:

X = A + B + C or X = A × B × C
Mixed: X = (A × B) + C or X = (A + B) − C
Power: X = √(A² + B² + C²)

3. Circular Puzzles

Sector logic: slices move clockwise/anti-clockwise — pattern x, x², x³… or x, x+2, x+4…
Opposite sector: number opposite n is n², n³, or n×k

4. Tree and Branch Puzzles (Flowcharts)

Two upper nodes point to a lower node → lower is usually sum/product/difference of upper two.

Formula: Bottom = (Left × Right) − Constant

Upper nodes combine (× then − constant) to form the lower node. Verify on two branches before predicting the third.

Part B: Analytical Reasoning — Seating Arrangements

Arrange variables P,Q,R,S… in positions by constraints. Fix one position first (no start in a circle).

1. Linear Arrangement (Row)

Facing	Left / Right
North (standard)	Left is your left; right is your right
South (flipped)	Left ↔ Right swap

"At extreme end": position 1 or n
"Adjacent to B": AB or BA (two orders)
"Second to right of B": B _ A (one person between)

2. Circular Arrangement

Facing	Directions
Center (inward)	Right = anti-clockwise, Left = clockwise
Outwards	Right = clockwise, Left = anti-clockwise

No start/end in a circle — fix one person to define relatives.

Linear: left/right is literal. Circular: facing decides clockwise vs anti-clockwise.

Solving Strategy

For Number Puzzles

Check magnitude: result much larger → multiplication, squares, cubes.
Check for primes: odd, not fitting tables → primes.
Trial & error (disciplined): apply rule to first completed set → if holds, test on second set → only if both hold, apply to missing set.

For Seating Arrangements

Direct first: place fixed points ("A is in the middle", "at an end") first.
Negative info: "B is NOT next to C" eliminates possibilities — note it.
Case method: if a clue has two possibilities (e.g., "A at an end"), draw both Case 1 and Case 2, eliminate the one that contradicts later clues.

Summary of Variables and Symbols

Symbol	Meaning
`n`	Number in sequence / position
`d`	Difference
`x², x³`	Perfect squares and cubes
`L / R`	Left / right
`CW / ACW`	Clockwise / anti-clockwise

Matrix: Row1 4+6=10, Row2 5+3=8, Row3 2+7=?

Triangle vertices A,B,C → center X = A×B + C. A=6,B=4,C=4 → X?

Tree: top nodes 6 and 4 give 20 via (× then −4). Top nodes 5 and 3 give?

Result much larger than inputs → likely?

Linear row facing North: left is?

Linear row facing South: left becomes?

“A is at extreme end” means?

Circular, facing center: right is?

Best first step for seating puzzles?

Notes

Visual Puzzles :-

Matrix ⇒ row/col sum/diff/product or √(A+B) ; test row-wise then col-wise

Triangle ⇒ center = A+B+C or A×B+C or √(A²+B²+C²)

Circle ⇒ sector ×/square or opposite n→n² ; Tree ⇒ bottom = left×right − k

Check magnitude → ×/square ; primes if odd & no table fits ; verify on 2 sets before missing

Seating :-

Linear North: left=left ; South: left↔right swap

Extreme→1 or n ; Adjacent→AB/BA ; Second to right: B _ A

Circular: center→right ACW/left CW ; outwards swapped ; fix one first

Strategy :-

Direct info first ; negatives for elimination ; case method for ambiguous “at an end” (draw both, kill one)

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