Logical Number Puzzles
Finding and applying hidden rules in tables, grids, and balance puzzles
Explanation
What are Logical Number Puzzles?
These puzzles hide a rule or pattern in a table, grid, or set of examples. You must find the rule and apply it to find the missing value.
Function Machine Puzzles
A number goes in, gets transformed by a rule, and comes out.
Example: In: 3 → Out: 10 | In: 5 → Out: 16 | In: 7 → Out: ?
Try rule × 3 + 1: 3×3+1=10 ✓, 5×3+1=16 ✓ → 7×3+1 = 22
Table Puzzles
A table has rows and columns following an operation.
| Input | Rule A (×3) | Rule B (+5) |
|---|---|---|
| 4 | 12 | 9 |
| 7 | 21 | 12 |
| 10 | 30 | 15 |
Balance / Scale Puzzles
Two sides of a scale are equal — use algebra-like thinking to find symbol values.
Example: ■ + ■ + ● = 20 | ■ + ● = 13
Subtract equation 2 from equation 1: ■ = 7 → then ● = 13 − 7 = 6
Strategy
- Test simple rules first: +, −, ×, ÷.
- If simple rules don't fit, try compound rules: ax + b.
- Once identified, verify the rule against ALL given examples.
- Apply the rule to find the unknown value.
Key Tips
- Start by looking at the simplest relationships (is one number double another?)
- For balance puzzles, eliminate one variable at a time using subtraction
- Always verify your rule works for all given pairs — one match can be coincidence
- For matrix/grid puzzles, check whether the rule applies to rows, columns, or both
Sample Practice Questions
-
A function machine applies ×4 then −3. Input = 5. What is the output?
Show answer
Answer: 17
-
If you have 3 apples and take away 2, how many do you have?
Show answer
Answer: 2
-
In a grid, rows and columns all add to 18. One row reads: 4, 7, ___. What fills the blank?
Show answer
Answer: 7
-
A balance shows ■ + ■ + ■ = ● + ●. If ● = 6, what is ■?
Show answer
Answer: 4
Practice Questions
Test your knowledge of Logical Number Puzzles with a timed quiz. Answers are revealed at the end.
Take Quiz →Frequently Asked Questions
What does Logical Number Puzzles cover in the Selective Entry Numerical Reasoning exam?
Finding and applying hidden rules in tables, grids, and balance puzzles.
How can I practise Selective Entry Numerical Reasoning Logical Number Puzzles questions for free?
Practise free Selective Entry Numerical Reasoning Logical Number Puzzles questions with instant answers and explanations on Safe Learning for Kids — no sign-up required.