Number Puzzles and Logic Set E
Number Puzzles and Logic Set E is a practice set covering the non-routine 11+ maths questions that test reasoning rather than one taught method: missing-digit puzzles, number sequences, balance or equation puzzles, and clue-based deduction problems. These question types appear throughout GL Assessment and CEM-style papers and reward a systematic approach over guessing.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify which puzzle type each question is (sequence, missing digit, balance, or clue-based deduction) before choosing a strategy.
- For a sequence, find the rule connecting consecutive terms (add, subtract, multiply, or a changing gap) by comparing at least three consecutive terms.
- For a missing-digit puzzle, work from the column where you have the most information, often the units column, and use trial values that satisfy that column first.
- For a balance or equation puzzle, treat both sides as equal and apply the same operation to both sides to isolate the unknown, exactly like a simple algebra equation.
- For a clue-based deduction puzzle, list every clue, then build a table of possibilities and eliminate options that break a clue.
- Substitute your final answer back into the original puzzle to check it satisfies every condition given.
- If a puzzle has more than one unknown, solve for the one with the most clues attached to it first.
Worked example
In this puzzle, the same shape always stands for the same number. Triangle + Triangle + Triangle = 18. Triangle + Square = 11. Find the value of Square.
- From the first equation, find the value of one Triangle: 18 / 3 = 6.
- Substitute Triangle = 6 into the second equation: 6 + Square = 11.
- Solve for Square: Square = 11 - 6 = 5.
- Check both equations: 6 + 6 + 6 = 18 (correct) and 6 + 5 = 11 (correct).
Practice questions
Try each question, then tap to reveal the answer.
Q1Find the next number in the sequence: 2, 6, 18, 54, ...Show answer
Answer: Each term is multiplied by 3: 54 x 3 = 162.
Q2Find the missing digit: 4_7 + 235 = 682.Show answer
Answer: 4_7 = 682 - 235 = 447, so the missing digit is 4.
Q3If Circle x 4 = 28, find the value of Circle x Circle.Show answer
Answer: Circle = 28 / 4 = 7. Circle x Circle = 7 x 7 = 49.
Q4Find the next term: 100, 91, 83, 76, ...Show answer
Answer: The gap decreases by 1 each time (9, 8, 7...), so the next gap is 6: 76 - 6 = 70.
Q5Three children, Amy, Ben and Cara, have ages that total 33. Ben is twice as old as Amy. Cara is 3 years older than Ben. If Amy is 6, find Ben's and Cara's ages.Show answer
Answer: Ben = 2 x 6 = 12. Cara = 12 + 3 = 15. Check: 6 + 12 + 15 = 33.
Q6Find the next number: 5, 10, 9, 18, 17, 34, ...Show answer
Answer: The pattern alternates: multiply by 2, then subtract 1. After 34, subtract 1: 34 - 1 = 33.
Q7A code shows A=1, B=2, C=3 and so on. What number does the word 'BAD' represent if you add the values of its letters?Show answer
Answer: B=2, A=1, D=4. Sum = 2 + 1 + 4 = 7.
Q8Two numbers have a sum of 20 and a difference of 4. Find the two numbers.Show answer
Answer: Larger = (20 + 4) / 2 = 12. Smaller = (20 - 4) / 2 = 8. Check: 12 + 8 = 20 and 12 - 8 = 4.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
In this puzzle, each letter stands for a single digit. AB x 3 = 96, where AB is a two-digit number with tens digit A and units digit B. Find the value of A and the value of B.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Four friends, Dan, Eve, Finn and Gita, sit in a row of four numbered seats, 1 to 4, from left to right. Use these clues to find who sits in each seat: Finn sits in seat 3. Gita sits directly to the left of Finn. Dan sits somewhere to the left of Eve.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the number puzzles and logic set e worksheet pack - 11 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 18 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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