MindProofMindProof · Puzzle guides
How to solve Target Number puzzles
Combine four numbers using arithmetic, parentheses and exact fractions. Follow checked Target Number examples and play the matching puzzles.
Target Number asks you to build an arithmetic expression that equals a target. You are constructing an answer, so more than one expression may be correct. MindProof’s web game checks your calculation and the numbers you used; it accepts all expressions allowed by its grammar, not just the example solution.
The web game’s rules
- Use each of the four displayed numbers exactly once. If a number appears twice, use both copies.
- You may add, subtract, multiply, divide and use parentheses. Type +, −, ×, ÷ or the keyboard forms -, * and /.
- Fractional, zero and negative intermediate results are allowed. Division by zero is not.
- Do not concatenate tiles: 3 and 3 cannot become 33. Do not introduce extra numbers, powers, factorials or decimal literals.
- Your final result must equal the target exactly. The web checker uses fractions internally, so repeating decimal approximations are unnecessary.
These rules describe the website. The native app uses a tile-combining game with different restrictions: intermediate tiles must be positive whole numbers, and reaching the target can leave unused tiles. Read the instructions in the version you are playing.
Start from the target
Think of simple factor pairs or sums. For 42, try 6 × 7. For 25, try 30 − 5. Then ask whether the available tiles can make those pieces without using a tile twice. A written inventory helps: cross out each tile as you place it.
1. Build two useful groups
Numbers: 2, 3, 4, 8. Target: 42.
(8 − 2) × (3 + 4) = 6 × 7 = 42
Subtraction makes 6; addition makes 7. Parentheses ensure both groups are evaluated before multiplication. All four tiles appear once.
2. Overshoot, then subtract
Numbers: 3, 4, 5, 6. Target: 25.
(6 + 4) × 3 − 5 = 10 × 3 − 5 = 25
It is often easier to make a nearby number. Here, 30 is one subtraction away from 25. The final 5 is a displayed tile, not an extra constant.
3. Fractions can make a larger answer
Numbers: 1, 3, 4, 6. Target: 24.
6 ÷ (1 − 3 ÷ 4) = 6 ÷ (1/4) = 24
First calculate 3 ÷ 4. Subtract that fraction from 1 to get one quarter. Dividing 6 by one quarter gives 24. Enter 6/(1-3/4); do not replace the denominator with a new decimal tile.
4. Repeated tiles still have separate uses
Numbers: 3, 3, 8, 8. Target: 24.
8 ÷ (3 − 8 ÷ 3) = 8 ÷ (1/3) = 24
The denominator is 3 − 8/3 = 1/3. One 8 is the numerator and the other belongs inside the denominator. Likewise, both copies of 3 are used once. Exact fractions avoid the rounding error in 2.6667.
Common mistakes and useful checks
- Missing parentheses.
6/1-3/4means 6 − 3/4, not 6 divided by 1 − 3/4. - Reusing a tile. A correct result is insufficient if the expression uses the wrong inventory.
- Rejecting fractions too early. A fraction in the middle can lead to a whole target.
- Assuming there is only one solution. Different valid operation orders are accepted. The revealed solution is an example.
Try a puzzle
Use the Target Number player. You can type or tap the on-screen number and operator buttons, press Enter to check, and ask for a hint before revealing one solution. For a different kind of reasoning, explore number series patterns or choose a game at the puzzle picker.