Logic and Puzzle Problems
Logic and puzzle problems are 11+ maths questions that use reasoning rather than a single calculation, such as finding number sequences, solving clue-based deduction puzzles, decoding letter or number ciphers, or working out balance-scale puzzles. They appear throughout GL Assessment and CEM-style maths papers and reward clear, step-by-step working.
Before you start
Make sure you're comfortable with these topics first:
Method
- List every clue or piece of given information separately before trying to solve anything.
- Identify the puzzle type (sequence, deduction, code, or balance) so you pick the right strategy.
- Build a table or list of possibilities for deduction puzzles, then cross off options using each clue in turn.
- Find the rule connecting one term to the next for sequences, then apply it forward or backward.
- Work out the letter-shift or value rule from any example given for codes, then apply it consistently.
- Check every original clue against your final answer to make sure nothing is contradicted.
Worked example
Five years ago, Maya was four times as old as her brother Ryan. In three years' time, Maya will be twice as old as Ryan. How old is Maya now?
- Let M stand for Maya's age now and R stand for Ryan's age now.
- Five years ago: M - 5 = 4(R - 5), which simplifies to M = 4R - 15.
- In three years: M + 3 = 2(R + 3), which simplifies to M = 2R + 3.
- Set the two expressions for M equal: 4R - 15 = 2R + 3, so 2R = 18 and R = 9.
- Substitute back to find M = 2 x 9 + 3 = 21.
- Check both conditions: five years ago, 16 = 4 x 4 is correct; in three years, 24 = 2 x 12 is correct. Final answer: Maya is 21 and Ryan is 9.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Four children - Zoe, Ali, Ben and Nina - each own a different pet: a fish, a guinea pig, a snake and a parrot. (1) Zoe does not own the fish or the snake. (2) Ali owns the parrot. (3) Ben's pet is not the guinea pig. (4) Nina does not own the fish. Match each child to their pet.
In a number code, a letter's value is found using 3n - 2, where n is its position in the alphabet (A = 1, B = 2, and so on). For example, the word BAD has value: B = 3 x 2 - 2 = 4, A = 3 x 1 - 2 = 1, D = 3 x 4 - 2 = 10, total = 4 + 1 + 10 = 15. (a) Find the total code value of the word FIG. (2) (b) A three-letter word has the form D_T. Its first letter has value 10, its last letter has value 58, and the total code value of the whole word is 111. Find the missing middle letter. (3)
There are 12 identical-looking balls, one of which is heavier than the rest. You have a balance scale and may use it at most 3 times. Describe a method that is certain to find the heavier ball.
Free printable worksheet
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