Lessons / Logical reasoning
Logical reasoning · Day 11

Puzzles

Make a grid (people × attributes) and fill ticks and crosses. A puzzle is solved by elimination, not inspiration.

Practise (4 questions) Present as slides

Why this topic matters

Floor puzzles and number puzzles are seating puzzles in another shape. Build a grid and fill it clue by clue.

Puzzle sets carry many marks. A table with one row per person or floor keeps every clue visible.

Floor puzzles: build the building

Draw the floors with 1 at the bottom (unless the question says the top floor is 1). Place the fixed clues first ('P lives on floor 3'), then the relative ones ('Q lives just above R').

Keep two versions when a clue allows two positions, and let the next clue decide.

floor 5Tfloor 4Qfloor 3Pfloor 2Rfloor 1S
Five floors, one person each: S R P Q T from the bottom
Example 1Five people P, Q, R, S, T live on floors 1 to 5 (1 at the bottom), one per floor. P is on floor 3. Q lives immediately above P. R lives immediately below P. S is not on the top floor. Who lives on floor 5?
  1. P = 3, Q = 4, R = 2.Fixed clue first, then the two neighbours.
  2. Floors 1 and 5 remain for S and T. S is not on top, so S = 1.
  3. T lives on floor 5.

Formula summary

Grid
Rows = people, columns = floors/days/colours.
Definite first
Place 'X lives on the top floor' clues before 'X is above Y' clues.
Floor puzzles
Floor 1 = bottom unless told otherwise. 'Above' does not mean 'immediately above'.
Number puzzles
Set up equations: sum, difference, product - then check options.

Shortcuts and tricks

Floor puzzle order

Use it when: 5 people, 5 floors.

  1. Write floors 5 to 1 vertically.
  2. Place the fixed ones, then the 'immediately above/below', then the rest.
ExampleA is on the top floor. C is immediately below A. E is on floor 1. B is above D. Who is on floor 3?
  1. A5, C4, E1.
  2. B above D in floors 2-3 → B3, D2.

Before you move on, you should be able to...

  • build a table before reading the second clue
  • place fixed clues first
  • branch when a clue allows two positions

Practice questions (4)

Try each one before opening the solution. Or practise them one by one so your score is saved.

easy The sum of two numbers is 60 and their difference is 14. Larger number?
  1. (60 + 14)/2.

Answer: 37

medium In a group of cows and hens there are 48 heads and 140 legs. How many cows?
  1. All hens: 96 legs. Extra 44 / 2 = 22 cows.

Answer: 22

medium P, Q, R, S, T live on floors 1-5 (1 = bottom). T is on floor 2. Q is immediately above T. R is on floor 1. S is above P. Who is on floor 5?
  1. T2, Q3, R1.
  2. P and S take 4 and 5; S above P → S5.

Answer: S

hard Three consecutive even numbers add to 138. The largest?
  1. Middle 46.

Answer: 48

Class plan (2 hours, for trainers)

A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.

10 minWarm-up.
35 minFloor puzzles with a table.
30 minTwo-attribute puzzles (person, city, job) with a grid.
40 minPractice set.
5 minRecap.
← Statements: Assumptions and ConclusionsOdd One Out / Classification →
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