Logical Number Puzzles

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.

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

1. Test simple rules first: +, −, ×, ÷.
2. If simple rules don't fit, try compound rules: ax + b.
3. Once identified, verify the rule against ALL given examples.
4. 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