Target 24 strategy guide

The rules of Target 24 fit in one sentence: use four given numbers, each exactly once, with addition, subtraction, multiplication and division, to make exactly 24. The puzzle is old — it has been a classroom favourite for decades — because it rewards a kind of thinking that plain arithmetic drills don’t: planning several steps ahead and working backwards from a goal. In BRINXO it is the Number Forge mode.

Why 24?

24 has more ways to be built than almost any small number. It has many factor pairs — 1 × 24, 2 × 12, 3 × 8 and 4 × 6 — and it is also a sum of friendly numbers such as 20 + 4, 18 + 6 and 12 + 12. More routes to the target means most sets of four numbers have at least one solution.

Strategy 1: aim for a factor pair

Most solutions end with a multiplication. Look at your four numbers and ask: can I make a 3 and an 8? A 4 and a 6? A 2 and a 12?

• 2, 3, 4, 7: make 6 with 7 − 3 + 2, keep the 4 → (7 − 3 + 2) × 4 = 24
• 1, 3, 4, 6: 4 × 6 is right there, but the 1 and the 3 can’t be made to vanish (3 − 1 = 2, 3 ÷ 1 = 3). The only solution uses a fraction: 6 ÷ (1 − 3/4) = 6 ÷ ¼ = 24 (see strategy 4).
• 5, 5, 2, 2: (5 + 5 + 2) × 2 = 24

Strategy 2: work backwards from 24

Pick one of your numbers and ask what the other three must make. If you hold a 3, the rest must make 8 (to multiply) or 21 (to add) or 27 (to subtract from). Checking a few of these “missing numbers” is much faster than trying combinations at random.

• 3, 8, 8, 9: hold the 3 — can 8, 8, 9 make 8? Yes: 8 × (9 − 8) = 8 → 3 × 8 = 24
• 6, 9, 9, 1: hold the 6 — can 9, 9, 1 make 4? Not easily. Make 18 + 6 instead: 9 + 9 = 18, 18 × 1 + 6 = 24

Strategy 3: use the spare numbers to make 1 or 0

When two numbers already make 24, the other two must not change it. Turn them into ×1 (a ÷ a, or the difference of consecutive numbers) or +0 (a − a).

• 4, 6, 5, 5: 4 × 6 × (5 ÷ 5) = 24
• 3, 8, 7, 7: 3 × 8 + (7 − 7) = 24

Strategy 4: fractions for the hardest puzzles

Some sets have no whole-number route at all. The trick is to create a fraction on purpose and then divide by it. These are the puzzles that stump most people.

• 3, 3, 8, 8: 8 ÷ (3 − 8/3) = 8 ÷ (1/3) = 24
• 1, 5, 5, 5: 5 × (5 − 1/5) = 5 × 24/5 = 24
• 3, 3, 7, 7: (3/7 + 3) × 7 = 3 + 21 = 24
• 4, 4, 10, 10: (10 × 10 − 4) ÷ 4 = 96 ÷ 4 = 24

A useful signal: if you have a pair like 8 and 3 and the obvious 8 × 3 leaves two numbers you cannot neutralise, try dividing by a fraction built from those two.

A practice routine

1. Scan for a factor pair first (3 × 8, 4 × 6, 2 × 12). That alone solves most puzzles.
2. Then work backwards: hold each number in turn and name the missing value.
3. Then try neutralising a spare pair to ×1 or +0.
4. Only then reach for fractions.

Following the same order every time is what makes you fast: you stop searching randomly and start checking a short list.

Playing Target 24 in BRINXO

In Number Forge you combine two numbers at a time: tap a number, an operation and another number, and they merge. Keep going until one number remains. Each round has five puzzles, every puzzle has at least one solution, and a hint can show you a good next move — at the cost of some points. Try it at brinxo.online/play.