Thinking Skills · Module 10
Logical Deduction
Work out the truth from clues, like a detective — ordering, chains, grids and seating, with four tiers of practice.
Page 1 · Introduction
Logical deduction
Logical deduction is working out the truth from a set of clues — like a detective. "Who owns the cat? Who sits in the middle?" You're given facts, and you piece together the answer.
The good news: there's a reliable method. You don't guess — you eliminate what can't be true until only the answer is left.
The big ideaUse each clue to rule things out. When only one possibility survives, that's your answer.
💡We build from simple ordering up to full grid puzzles. Take each clue one at a time — that's the secret to never getting lost.
On the real testWhere this appearsDeduction puzzles are core to the Thinking Skills section (25% of your mark, from 2025). The test lists "finding procedures" and reasoning from information — exactly this.
Page 2 · Ordering clues
Putting things in order
The simplest deductions arrange people or things in a line — by height, age, position and so on.
Tom is taller than Sam. Sam is taller than Ben. Who is shortest?
Line them up tallest to shortest: Tom > Sam > Ben.
Ben
The method
Draw a line and place each person as you read each clue. Once they're all placed, read off the answer.
✅Write the order down — don't try to hold it all in your head. A quick sketch prevents mistakes.
Page 3 · If-then chains
Following the chain
Some clues link together in a chain. Follow them one link at a time, in one direction only.
If it rains, the match is cancelled. If the match is cancelled, we go to the cinema. It rained. What happened?
Rain → match cancelled → cinema. Follow the arrows: we went to the cinema.
They went to the cinema
CarefulChains only work one way. "We went to the cinema" does NOT prove it rained — there might be other reasons. Follow the arrows forward, never backward.
Page 4 · The grid method
Matching things up
When you must match people to things (sport, pet, colour), use elimination.
Kim, Lee and Max each play one sport: tennis, chess or swimming. Kim plays neither tennis nor chess. Lee plays chess. Who plays what?
Lee = chess (given). Kim isn't tennis or chess, so Kim = swimming. That leaves Max = tennis.
Kim swims, Lee chess, Max tennis
💡Start with the most definite clue ("Lee plays chess"). Lock it in, then everything else falls into place by elimination.
Page 5 · Using "not"
Clues that tell you what ISN'T
Negative clues ("does not", "never") are just as powerful — they cross off possibilities.
Ann, Bob and Cara own a cat, a dog and a fish. Ann's pet has no fur. Bob owns the dog. Who owns the cat?
Bob = dog. Ann's pet has no fur, so Ann isn't the cat or dog → Ann = fish. That leaves Cara = cat.
Cara owns the cat
✅Turn a "not" into progress: "Ann's pet has no fur" quietly tells you Ann has the fish. Read negatives as clues, not obstacles.
Page 6 · Seating & position
Who sits where?
Position puzzles are ordering puzzles with a twist — "next to", "left of", "between". Draw the seats.
Five seats in a row. Ann is in the middle. Bea is immediately to Ann's left. Which seat is Bea in?
Middle of 5 is seat 3, so Ann = seat 3. Immediately left = seat 2. Bea = seat 2.
Seat 2
💡Draw the row of seats as empty boxes and fill them in. "Left" and "right" are from the people's point of view unless told otherwise.
Page 7 · Practice
Level 1 · Easy
Warm up
Simple ordering. Sketch the line, then read the answer. Tap to check.
1. Amy finished before Bea. Bea finished before Cy. Who won?
A Cy
B Bea
C Amy
D Can't tell
Order: Amy, then Bea, then Cy. Amy finished first — she won.
2. The red box is left of the blue box. The blue box is left of the green box. Which box is on the far right?
A Red
B Green
C Blue
D Can't tell
Left to right: Red, Blue, Green. Green is on the far right.
3. Dan is older than Eve. Eve is older than Fay. Who is youngest?
A Fay
B Eve
C Dan
D Can't tell
Oldest to youngest: Dan, Eve, Fay. Fay is youngest.
🎉Ordering puzzles are just careful line-ups. Now let's match things together.
Page 8 · Practice
Level 2 · Medium
Matching & negatives
Start with the most definite clue, then eliminate.
1. Jo, Ken and Liz have a red, blue or green bag. Ken's is blue. Jo's is not green. What colour is Liz's bag?
A Red
B Green
C Blue
D Can't tell
Ken = blue. Jo isn't green (and isn't blue), so Jo = red. That leaves Liz = green.
2. Three pets: cat, dog, bird belong to Sam, Tia, Uma. Sam's pet has feathers. Tia doesn't own the cat. Who owns the cat?
A Sam
B Tia
C Uma
D Can't tell
Sam = bird (feathers). Tia isn't the cat, so Tia = dog. That leaves Uma = cat.
3. Five seats in a row. Meg sits in the middle. Nia sits immediately to Meg's right. Which seat is Nia in (seats numbered 1–5 left to right)?
A Seat 4
B Seat 2
C Seat 5
D Seat 3
Middle = seat 3 = Meg. Immediately to her right = seat 4. Nia = seat 4.
💪Notice how a single "not" clue cracked each puzzle. Eliminating is more powerful than guessing.
Page 9 · Practice
Level 3 · Hard
Two-step deduction
These need you to combine two or three clues. Work them in order, locking in what you learn.
1. Four children by age: Dan older than Eve, Eve older than Fay, Fay older than Gus. Who is second oldest?
Order: Dan > Eve > Fay > Gus. Second oldest is Eve.
2. Ana, Bo and Cy sit in a row of 3. Ana is not in the middle. Bo sits immediately to the left of Ana. Who is in the middle?
A Ana
B Bo
C Cy
D Can't tell
Ana isn't in the middle, so Ana is on an end. Bo is immediately to Ana's left, which is only possible if Ana is on the right (seat 3) and Bo is seat 2. That leaves Cy in seat 1. The middle seat (2) is Bo.
3. If the alarm rings, everyone leaves. If everyone leaves, the room is empty. The alarm rang. Which MUST be true?
A The room is empty
B The room is full
C The alarm was broken
D Nobody heard it
Chain: alarm → everyone leaves → room empty. The alarm rang, so following the arrows, the room is empty.
💡The seating one is tricky — when a clue leaves options open, test them against the other clues until only one fits.
Page 10 · Challenge
Level 4 · Challenge
Think smart
Full deduction puzzles. Work through the clues in order and eliminate carefully.
1. Ann, Ben and Cat scored 70, 80 and 90 (in some order). Ann did not score highest. Ben scored more than Ann. Cat did not score 80. Ann scored more than 70. What did Ann score?
Ann isn't 90 (not highest) and isn't 70 (scored more than 70), so Ann = 80. Then Ben > Ann means Ben = 90, and Cat = 70 (and Cat isn't 80, which fits). Ann scored 80.
2. Three houses in a row are red, blue and yellow. The red house is not next to the yellow house. The blue house is in the middle... wait, which house is in the middle?
A Red
B Yellow
C Blue
D Can't tell
If red can't be next to yellow, something must separate them — so the middle house is blue, keeping red and yellow on the ends, apart. Middle = blue.
3. Four runners: P beat Q. R beat P. Q beat S. R did not come last. Who came first?
R beat P, P beat Q, Q beat S: so R > P > Q > S. R came first. (The "R not last" clue confirms it, but the chain already shows R on top.)
🌟Full deduction puzzles reward patience and neat elimination. Cracking these is exactly the skill the Thinking Skills section is testing.
Complete
Sharp thinking!
You've completed the Logical Deduction module.
You can now order things from clues, follow if-then chains one way, match people to things by elimination, use negative clues, and crack seating and grid puzzles. The habit that ties it together: rule things out until only the answer remains.