Number Puzzles and Logic Set D
Number Puzzles and Logic Set D develops the reasoning skills behind 11+ number puzzles: working backwards from a result using inverse operations, systematically testing possibilities against several clues at once, and spotting number properties such as factors, multiples and digit patterns. These puzzles carry no context and cannot be solved by a single remembered formula, so a clear, methodical approach matters more than speed.
Method
- Read every clue or condition before starting, and list what is already known rather than guessing straight away.
- If the puzzle describes a sequence of operations leading to a known result, work backwards from that result, undoing each operation in reverse order using its inverse.
- For puzzles about a number's digits or properties, list the possibilities that satisfy one clue first, then check each of those against the remaining clues.
- Where no direct method exists, use trial and improvement, adjusting your next guess based on whether the previous one was too high or too low.
- Once you reach an answer, check it against every clue in the puzzle, not just the last one you used to find it.
- Show your working clearly, since answer-only responses cannot earn method marks on a multi-step puzzle.
Worked example
I think of a number. I double it, add 7, then divide by 3. My answer is 15. What was my original number?
- Work backwards from the final answer, undoing the last operation first: undo the division by 3 by multiplying: 15 x 3 = 45.
- Undo the addition of 7 by subtracting: 45 - 7 = 38.
- Undo the doubling by halving: 38 / 2 = 19.
- Check by working forwards: 19 x 2 = 38, 38 + 7 = 45, 45 / 3 = 15, which matches.
- Final answer: 19.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1I think of a number, subtract 9, then multiply by 4. The result is 48. What was my number?Show answer
Answer: 21 (48 / 4 = 12, then 12 + 9 = 21)
Q2A number is a multiple of both 4 and 6, lies between 30 and 50, and has a digit sum of 9. What is the number?Show answer
Answer: 36 (multiples of 12 in range are 36 and 48; only 36 has a digit sum of 9)
Q3Three consecutive numbers add up to 63. What is the largest of the three numbers?Show answer
Answer: 22 (the numbers are 20, 21 and 22)
Q4A two-digit number has a tens digit that is twice its units digit, and the digits add up to 9. What is the number?Show answer
Answer: 63 (units = 3, tens = 6, since 6 + 3 = 9 and 6 = 2 x 3)
Q5I think of a number, add 15, then halve it. My answer is 20. What was my original number?Show answer
Answer: 25 (20 x 2 = 40, then 40 - 15 = 25)
Q6Working backwards: a number is multiplied by 3, then 8 is subtracted, giving 25. What was the original number?Show answer
Answer: 11 (25 + 8 = 33, then 33 / 3 = 11)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
I think of a number. I add 12, multiply the result by 2, then subtract 6. My final answer is 40. Use inverse operations, showing each step, to find my original number.
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A three-digit number is a multiple of 5, is even, has a hundreds digit of 4, and its digits add up to 12. Use these clues, showing your reasoning, to find the exact number.
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Free printable worksheet
Want more practice on paper? Download the number puzzles and logic set d 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 14 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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