Logic and Puzzle Problems: Practice Set 2
Logic and Puzzle Problems: Practice Set 2 gives further practice at the puzzle types tested in 11+ papers, including number sequences with more than one rule, deduction puzzles with several interlocking clues, letter codes, and problems that use overlapping groups such as pupils doing two clubs. It follows on from the first Logic and Puzzle Problems topic.
Method
- Read every clue or piece of information given before attempting to solve anything, and note whether the puzzle is a sequence, a deduction puzzle, a code, or an overlapping-groups puzzle.
- For a sequence with two operations, such as multiply then add, test your rule on at least two consecutive pairs of terms before applying it to find a missing term.
- For a deduction puzzle, draw a table linking every person, item or option mentioned, then use each clue in turn to rule out impossible combinations.
- For a code, work out the rule linking a letter, or a starting example, to its coded value, checking it against every example given before applying it to a new word.
- For a puzzle involving overlapping groups, work from the information about the overlap outwards to fill in each remaining region.
- Once you have an answer, check it against every clue or piece of given information in the question, not just the last one you used.
Worked example
Look at the sequence: 3, 7, 15, 31, 63, ... Each term is found by doubling the previous term and adding 1. Find the next term.
- Identify the rule connecting each term to the next: double the term, then add 1.
- Check the rule on an earlier pair: 7 x 2 + 1 = 15, which matches the given sequence.
- Apply the rule to the last given term, 63: 63 x 2 + 1.
- 63 x 2 = 126, then 126 + 1 = 127.
- The next term in the sequence is 127.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Look at this sequence: 2, 6, 18, 54, ... What is the next term?Show answer
Answer: 162 (each term is multiplied by 3: 54 x 3)
Q2In a class, 18 pupils play football, 14 play tennis, and 6 play both sports. How many pupils play at least one of the two sports?Show answer
Answer: 26 pupils (18 + 14 - 6, since the 6 who play both would otherwise be counted twice)
Q3In a code, each letter is replaced by the letter 3 places earlier in the alphabet (D becomes A, E becomes B, and so on, wrapping so C becomes Z). Decode the word FRJV.Show answer
Answer: COGS (shift each letter back 3 places: F to C, R to O, J to G, V to S)
Q4Four friends, Leo, Mia, Sam and Zara, each finished in a different position (1st, 2nd, 3rd, 4th) in a race. (1) Leo did not finish 1st or 4th. (2) Mia finished immediately before Sam. (3) Zara finished 1st. Find each person's finishing position.Show answer
Answer: Zara 1st, Leo 2nd, Mia 3rd, Sam 4th
Q5Look at this group of numbers: 16, 25, 36, 44, 49. Which number does not belong?Show answer
Answer: 44 (the others are all square numbers: 16 = 4^2, 25 = 5^2, 36 = 6^2, 49 = 7^2)
Q6In a magic square, every row, column and diagonal adds up to 15. The grid is: Row 1: 8, a, 6. Row 2: 3, 5, 7. Row 3: 4, 9, b. Find a and b.Show answer
Answer: a = 1 and b = 2 (Row 1 gives 8 + a + 6 = 15, so a = 1; Row 3 gives 4 + 9 + b = 15, so b = 2)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Look at the sequence: 1, 4, 13, 40, 121, ... Each term is found by multiplying the previous term by 3 and adding 1. (a) Show that the rule works for the third term. (b) Find the next term in the sequence.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
In a survey of 30 pupils, 19 like maths, 15 like science, and 8 like both subjects. (a) Calculate how many pupils like maths only. (b) Calculate how many like science only. (c) Calculate how many pupils like neither subject.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Three sisters, Amy, Beth and Cara, have ages that are three consecutive even numbers, n, n + 2 and n + 4. (1) Cara is the oldest. (2) The sum of all three ages is 42. (3) Beth is older than Amy. (a) Form an equation using n for the youngest age. (b) Solve your equation to find n. (c) State the three sisters' ages, matched to their names.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the logic and puzzle problems: practice set 2 worksheet pack - 12 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 2 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on logic and puzzle problems: practice set 2, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.