Building equations
Strategy card
Equation building is targeted search plus exact checking.
- Step 1: Use size, parity and last digits to prune options.
- Step 2: Respect order of operations and parentheses.
- Step 3: Compute candidates exactly; avoid mental shortcuts that skip signs.
- Step 4: Verify by substituting back.
Tip: Check the units digit first; it rules out many options instantly.
Worked example
Use every number and every sign once (× and ÷ before + and −). Which answer can you make?
Numbers and signs: 6 5 3 5 × − ÷
- A: 5 (the answer)
- B: 9
- C: 11
- D: 1
- E: 7
Why: 6 × 5 ÷ 3 − 5 = 5. None of the other answers can be made with these numbers and signs.
Your turn
Your turn 1 of 3
Use every number and every sign once (× and ÷ before + and −). Which answer can you make?
Numbers and signs: 5 3 8 1 × × −
Your turn 2 of 3
Use every number and every sign once (× and ÷ before + and −). Which answer can you make?
Numbers and signs: 8 11 4 10 − × ×
Your turn 3 of 3
Use every number and every sign once (× and ÷ before + and −). Which answer can you make?
Numbers and signs: 1 9 5 9 × × −
Keep practicing
Grown-ups: Ask how they'd explain their search strategy. Parent guide
Next lesson: Logic clues