Logic Grids and Deduction Puzzles Set F
A logic grid puzzle presents several clues about people, objects or preferences, such as names, pets or colours, and asks pupils to work out which items match up, usually recorded in a grid where rows and columns represent the different categories. 11+ papers test systematic elimination: marking off combinations a clue rules out, one step at a time, until every match is certain.
Method
- List all the categories and their items clearly, and draw or imagine a grid with one category along the top and another down the side.
- Read every clue once before starting, and mark any direct clue, such as 'Sam owns the dog', on the grid immediately as a confirmed match.
- Once a match is confirmed, cross out every other cell in that same row and that same column, since each item can only match one other item.
- Use indirect clues, such as 'the person with the cat is not Tom', to cross out impossible combinations rather than confirming matches straight away.
- Work through the clues repeatedly, since crossing out one impossible combination can reveal a direct match elsewhere, for example if only one cell remains un-crossed in a row.
- Check your finished grid against every clue given, to confirm no clue has been broken.
Worked example
Three friends, Amy, Ben and Cara, each have a different pet: a cat, a dog or a rabbit. Amy does not have the dog. Ben has the cat. Work out which pet Cara has.
- Set up a grid with Amy, Ben and Cara down the side, and cat, dog and rabbit across the top.
- Mark the direct clue: Ben has the cat, so tick Ben-cat, and cross out Ben-dog and Ben-rabbit.
- Since Ben has the cat, cross out Amy-cat and Cara-cat as well, since only one person can have each pet.
- Use the clue 'Amy does not have the dog' to cross out Amy-dog.
- Amy's only remaining option is rabbit, so tick Amy-rabbit, and cross out Cara-rabbit.
- Cara's only remaining option is dog, so Cara has the dog.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Two pupils, Leo and Mia, each choose a different drink: juice or water. Leo does not choose water. What does Leo choose?Show answer
Answer: Juice
Q2Three pupils, Ali, Beth and Cody, sit in a row of three seats. Beth is not at either end. Which position must Beth be in?Show answer
Answer: The middle seat
Q3Four friends each own a different colour bike: red, blue, green or yellow. Dan's bike is not red or blue. Ellie's bike is green. Which colour must Dan's bike be?Show answer
Answer: Yellow (green is taken by Ellie, and red and blue are ruled out for Dan, leaving only yellow)
Q4In a logic grid puzzle, once you know 'Tara has the drum', why can you immediately cross out every other instrument in Tara's row?Show answer
Answer: Because each person can only be matched to one instrument, so once Tara is confirmed to have the drum, she cannot also have any of the others.
Q5Three houses in a row are numbered 1, 2 and 3. The red house is not house 1. The blue house is house 3. Which house must be red?Show answer
Answer: House 2 (house 1 is ruled out and house 3 is blue, so house 2 is the only option left)
Q6Four pupils, W, X, Y and Z, each play a different sport. If three of the four pupil-sport pairings are already fixed by clues, how many more clues, at minimum, are needed to be certain of the last pairing?Show answer
Answer: None; once three pairings are fixed, the last one is known automatically by elimination.
Q7True or False: in a logic grid puzzle, a clue that only rules out one possibility, such as 'X does not like Y', can still be essential to solving the puzzle.Show answer
Answer: True
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Four friends, Priya, Quinn, Reo and Sam, each have a different favourite fruit: apple, banana, cherry or date. Priya's favourite is not apple or banana. Quinn's favourite is cherry. Sam's favourite is not apple. Work out each person's favourite fruit, explaining your reasoning at each step.
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Five books, coloured blue, yellow, green, purple and red, are placed in positions 1 to 5 on a shelf, left to right, one colour per position. The green book is in position 3. The red book is in position 5. The yellow book is immediately to the left of the green book. The blue book is immediately to the left of the yellow book. Work out which position the purple book is in, and state the colour of the book in every position.
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Free printable worksheet
Want more practice on paper? Download the logic grids and deduction puzzles set f worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 29 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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