Logic and Puzzle Problems - Worksheets, Questions and Revision

20 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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11+ · Numerical Reasoning and Logical Problem-Solving

EP.M15 Logic and Puzzle Problems

GL ASSESSMENT GL11-MATHS-LOGIC · Calculators not allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Look at the number sequence: 3, 7, 11, 15, ...
(a)State the rule used to get from one term to the next.(1)
(b)Write down the next two terms of the sequence.(2)
(Total for Question 1 is 3 marks)
2
Look at this group of numbers: 12, 18, 24, 30, 35, 42
  • A) 12
  • B) 18
  • C) 30
  • D) 35
  • E) 42
(Total for Question 2 is 2 marks)
3
Amelia is taller than Ben. Ben is taller than Chloe.
(Total for Question 3 is 2 marks)
4
In a code, every letter is replaced by the letter 3 places later in the alphabet (A becomes D, B becomes E, and so on), wrapping round so X becomes A, Y becomes B and Z becomes C.
(a)Decode the word PDWKV.(2)
(b)Use the same code to encode the word PUZZLE.(2)
(Total for Question 4 is 4 marks)
5
In a class of 30 pupils, 18 play football, 15 play cricket, and 7 play both football and cricket.
(a)Find the number of pupils who play football only, and the number who play cricket only.(3)
(b)How many pupils play neither football nor cricket?(2)
(Total for Question 5 is 5 marks)
6
Six friends - Priya, Jamal, Sofia, Tom, Aisha and Ben - sit at a round table with six evenly spaced seats, numbered 1 to 6 clockwise. Seats directly opposite each other differ by 3 (for example, seat 1 is opposite seat 4). Use these clues: (1) Sofia is directly opposite Tom. (2) Priya sits immediately clockwise of Sofia. (3) Ben sits immediately anticlockwise of Tom. (4) Aisha sits immediately clockwise of Tom. (5) Jamal is not seated immediately next to Priya.
(a)Complete the seating order, listing all six friends clockwise starting from Sofia.(3)
(b)State who sits directly opposite Jamal.(1)
(c)State who sits immediately anticlockwise of Aisha.(1)
(Total for Question 6 is 5 marks)
7
Six years ago, Grace was three times as old as her brother Leo. In four years' time, Grace will be twice as old as Leo.
(Total for Question 7 is 4 marks)
8
A sequence is formed using the rule 'multiply by 2, then subtract 3', starting at 5: 5, 7, 11, 19, ...
(a)Find the next two terms of the sequence.(2)
(b)Explain why every term in this sequence will always be an odd number.(2)
(Total for Question 8 is 4 marks)
9
Four pupils - Noah, Freya, Isaac and Maya - each own a different pet: a cat, a dog, a hamster and a rabbit. (1) Noah does not own the cat or the dog. (2) Freya owns the rabbit. (3) Isaac's pet is not the hamster. (4) Maya does not own the cat.
(Total for Question 9 is 4 marks)
10
A rule connects pairs of numbers: 3 is linked to 11, and 5 is linked to 21.
(a)Find the rule connecting the number n to its linked value, giving your answer in the form an+b.(2)
(b)Using your rule, find the value linked to 8.(1)
(c)Find the value of n whose linked value is 56.(2)
(Total for Question 10 is 5 marks)
11
There are 8 identical-looking coins, but one of them is a fake that is lighter than the rest. You have a balance scale and may use it only twice.
(Total for Question 11 is 4 marks)
12
On an island, Knights always tell the truth and Knaves always lie. You meet two islanders, X and Y. X says: 'At least one of us is a Knave.'
(Total for Question 12 is 3 marks)
13
In this 3 by 3 grid, every row and every column adds up to 15: Row 1: 2, 7, 6. Row 2: 9, a, 1. Row 3: 4, 3, b.
(a)Find the value of a.(2)
(b)Find the value of b.(2)
(Total for Question 13 is 4 marks)
14
If 15th July 2026 falls on a Wednesday, what day of the week is 2nd August 2026?
(Total for Question 14 is 3 marks)
15
In a number code, a letter's value is found using 2n+1, where n is its position in the alphabet (A=1, B=2, ...). For example, the word CAB has value 7+3+5=15.
(a)Find the total code value of the word FED.(2)
(b)A three-letter word has the form C _ T. Its first letter has value 7, its last letter has value 41, and the total code value of the whole word is 79. Find the missing middle letter.(3)
(Total for Question 15 is 5 marks)
16
In a school race with runners David, Zara, Oliver, Priya and Ethan: Oliver finished before Priya but after Zara. Priya finished before Ethan. Zara did not finish first. David finished immediately before Zara.
(Total for Question 16 is 4 marks)
17
Five friends - Ravi, Beth, Callum, Dara and Elowen - each play a different sport: Football, Tennis, Swimming, Rugby and Athletics. (1) Ravi's sport comes alphabetically before Beth's sport. (2) Callum does not play Football or Rugby. (3) Dara plays Swimming. (4) Beth does not play Tennis. (5) The person who plays Athletics has a name starting with a vowel.
(Total for Question 17 is 4 marks)
18
The value of a word is found by adding the alphabet positions of its letters, then multiplying by the number of letters in the word. For example, CAT: C=3, A=1, T=20, sum=24, letters=3, value=24x3=72.
(a)Find the value of the word MATHS.(3)
(b)Which has the greater value: SUM or ADD? Show your working.(3)
(Total for Question 18 is 6 marks)
19
There are 9 identical-looking marbles, one of which is heavier than the rest. You have a balance scale and may use it only twice.
(Total for Question 19 is 4 marks)
20
Four sealed boxes P, Q, R and S each contain a different number of sweets, using the numbers 4, 7, 10 and 13 once each. (1) Box P has more sweets than Box Q. (2) Box R has fewer sweets than Box S. (3) Box S contains 3 more sweets than Box P. (4) Box Q does not contain 4 sweets.
(Total for Question 20 is 5 marks)
Mark scheme · EP.M15 Logic and Puzzle Problems

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20