How to Answer 11+ Logic Problems

Logic problems are the puzzle stories of the 11+. A few short lines of clues — who has how many, who finished where, which floor someone lives on — then one question. They are among the longest questions on the paper, and they look harder than they are.

Here is the secret: you never need clever maths. Every clue is one small step — add 3, halve it, move up two floors. The real skill is order. The clues are deliberately jumbled, so the line you read first is often the line you must use last.

The method

Read every clue. Each line is one fact. Count what you have before you start.
Find the clue you can use straight away. One clue always holds a solid starting point: a real number ("Anya finished in 18 seconds") or a fixed fact ("the trip is on Friday"). Start there, even if it is the last line.
Deal with one clue at a time — completely. Work out what it tells you, write the number down, then move on. Don't try to hold it all in your head.
Rule out whatever each fact makes impossible. In harder puzzles a clue gives no number straight away, but it shrinks the possibilities. The answer is whoever survives every fact.
Check who the question is actually about. The wrong options are usually the right numbers for the wrong people.

Worked examples

Example 1: a chain of numbers

A bookcase has six shelves, numbered 1 at the bottom to 6 at the top. The atlas is on shelf 2. The dictionary is three shelves above the atlas. The comic is two shelves below the dictionary. The annual is one shelf above the comic.

Which shelf is the annual on?

A. 3 B. 5 C. 4 D. 6

Start with the atlas — the clue with a real number. Chain outwards, one clue at a time: the dictionary is on shelf 2 + 3 = 5, the comic on shelf 5 − 2 = 3, and the annual one above that: 3 + 1 = 4.

Now test every option:

A. 3 — the comic's shelf. The annual sits one shelf above it, not on it. ✗
B. 5 — the dictionary's shelf. ✗
C. 4 — one shelf above the comic. Fits every clue. ✓
D. 6 — no clue puts anything on the top shelf. ✗

The answer is C. 4.

Example 2: watch the direction words

In a race, Anya finished in 18 seconds. Ben finished 4 seconds faster than Anya. Chloe finished 2 seconds slower than Ben and 1 second faster than Dan.

How many seconds did Dan take?

A. 13 B. 15 C. 19 D. 17 E. 21

The solid start is Anya: 18 seconds. Faster means fewer seconds, so Ben took 18 − 4 = 14, and Chloe, 2 seconds slower, took 14 + 2 = 16. Chloe was 1 second faster than Dan — so Dan was 1 second slower: 16 + 1 = 17.

Test every option against the Chloe clue: she took 16 seconds and is exactly 1 second faster than Dan.

A. 13 — would make Chloe 12 seconds. Chloe took 16. ✗
B. 15 — this is 16 − 1, subtracting the last second instead of adding it. ✗
C. 19 — would make Chloe 18 seconds, the same as Anya. ✗
D. 17 — Chloe (16) is exactly 1 second faster than Dan (17). ✓
E. 21 — would make Chloe 20 seconds. ✗

The answer is D. 17.

Example 3: when no clue gives a number straight away

During activities week, Class 6 has one event each day from Monday to Friday: a rehearsal, a concert, a bake sale, a quiz and a trip. The trip is on Friday. The bake sale is the day after the concert. The rehearsal is two days before the concert.

On which day is the quiz?

A. Monday B. Wednesday C. Tuesday D. Thursday E. Friday

The strongest clue is the fixed one: the trip is on Friday. Both other clues hang off the concert, so ask which day the concert can be. Not Thursday — the bake sale would land on the taken Friday. Not Monday or Tuesday — the rehearsal, two days earlier, would fall off the timetable. So the concert is Wednesday, the rehearsal Monday, the bake sale Thursday — and the quiz takes the one day left.

Test every option:

A. Monday — the rehearsal's day. ✗
B. Wednesday — the concert's day. ✗
C. Tuesday — the only empty day. ✓
D. Thursday — the bake sale's day. ✗
E. Friday — the trip's day. ✗

The answer is C. Tuesday.

The traps

The first clue often can't be used first. The clues are shuffled on purpose. If line 1 talks about people you know nothing about yet, skip it, find the line with a solid fact, and come back.
Holding it all in your head. Three or four half-remembered numbers will tangle. Jot each one down the moment you find it: "atlas 2, dictionary 5, comic 3".
Direction words flip the sums. Faster means fewer seconds; below means take away. Most wrong options are the number you get by flipping one direction the wrong way.

Try these yourself

Tom won 14 tokens at the fair. Sara won half as many tokens as Tom. Raj won 3 more tokens than Sara.

How many tokens did Raj win?

A. 8 B. 12 C. 10 D. 14 E. 6

In a block of flats, Aisha lives three floors above Ezra. Carys lives one floor below Aisha. Dylan lives two floors above Ezra. Elsie lives one floor below Dylan.

Which two people live on the same floor?

A. Aisha and Elsie B. Carys and Dylan C. Ezra and Elsie D. Aisha and Dylan E. Carys and Elsie

Five children queue for the water slide: Femi, Gus, Holly, Ivy and Jamal. Holly stands two places in front of Femi. Jamal stands directly behind Femi. Ivy is at the back.

Who is in the middle of the queue?

A. Gus B. Holly C. Femi D. Jamal E. Ivy

Answers

1. C. 10 — Sara won 14 ÷ 2 = 7 tokens, so Raj won 7 + 3 = 10.
2. B. Carys and Dylan — call Ezra's floor E: Aisha is on E + 3, so Carys and Dylan are both on E + 2.
3. C. Femi — Ivy is 5th and Jamal is directly behind Femi, so the only fit is Holly 1st, Gus 2nd, Femi 3rd, Jamal 4th.

The complete 11+ question-type guide
How to answer 11+ deduction questions — the other long question type: a block of facts, five sentences, and only one that must be true.

All example questions come from the Brainblox question bank — practise this question type inside 15 arcade games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.