Fours Challenge: Solve equations using exactly four 4s to reach target numbers.

Let’s solve each equation one by one, using exactly four 4s and only basic arithmetic: +, −, ×, , and parentheses.

We’ll go row by row.

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1. 4 4 4 4 = 3

Try: (4 + 4 + 4) ÷ 4
→ 12 ÷ 4 = 3 ✔

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2. 4 4 4 4 = 6

Try: (4 + 4) ÷ 4 + 4
→ 8 ÷ 4 = 2; 2 + 4 = 6 ✔
Or: 4 + (4 + 4) ÷ 4 → same thing.

Another way: (4 × 4 + 4) ÷ 4? → (16+4)/4=20/4=5 ✘
Stick with first: (4 + 4) ÷ 4 + 4 = 6

Wait — let’s check order of operations:

(4 + 4) ÷ 4 + 4 = 8 ÷ 4 + 4 = 2 + 4 = 6 ✔

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3. 4 4 4 4 = 7

Try: 4 + 4 - 4 ÷ 4
→ 4 + 4 = 8; 4 ÷ 4 = 1; 8 - 1 = 7 ✔

Yes! That works.

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4. 4 4 4 4 = 8

Easy: 4 + 4 + 4 - 4 = 8? → 12 - 4 = 8 ✔
Or: 4 × 4 ÷ 4 + 4? → 16 ÷ 4 = 4; 4 + 4 = 8 ✔
But simplest: 4 + 4 + 4 - 4 = 8

Actually, even simpler: 4 × 2 = 8, but we can’t use 2 directly. So stick with addition/subtraction.

4 + 4 + 4 - 4 = 8 ✔

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5. 4 4 4 4 = 24

Think: 4 × 6 = 24. Can we make 6 from three 4s?

Earlier we made 6 from two 4s: (4 + 4) ÷ 4 + 4? Wait no — that used four 4s already.

Wait — try: (4 + 4) × (4 - 4/4)? Let’s see:

4/4 = 1; 4 - 1 = 3; 4 + 4 = 8; 8 × 3 = 24 ✔ But that uses five 4s? No:

Breakdown: (4 + 4) × (4 - (4 ÷ 4)) → that’s five 4s! ✘

We must use exactly four 4s.

Try: 4 × 4 + 4 + 4 = 16 + 4 + 4 = 24 ✔ Yes!

Perfect.

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6. 4 4 4 4 = 28

Try: 4 × 4 + 4 × 4? → 16 + 16 = 32 ✘ too big.

Try: 4 × (4 + 4) - 4? → 4 × 8 = 32; 32 - 4 = 28 ✔

Check: 4 × (4 + 4) - 4 = 4×8 - 4 = 32 - 4 = 28 ✔

Uses four 4s: yes.

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7. 4 4 4 4 = 32

Try: 4 × 4 + 4 × 4 = 16 + 16 = 32 ✔

Exactly four 4s: yes.

Or: (4 + 4) × 4 = 8 × 4 = 32, but that’s only three 4s — need to use all four.

So better: 4 × 4 + 4 × 4 = 32 ✔

Alternatively: (4 × 4) × (4 ÷ 4) × something? Not needed.

First solution is fine.

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8. 4 4 4 4 = 48

Try: 4 × 4 × 3 = 48 — can we make 3 from two 4s? Earlier: (4 + 4 + 4) ÷ 4 = 3 — but that uses four 4s already.

Wait — try: (4 + 4) × (4 + 4) / something? 8 × 8 = 64 — too big.

Try: 4 × (4 + 4 + 4) = 4 × 12 = 48 ✔

That’s: 4 × (4 + 4 + 4) — uses four 4s: one outside, three inside → total four ✔

Perfect.

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Now let’s write them cleanly:

1. (4 + 4 + 4) ÷ 4 = 3
2. (4 + 4) ÷ 4 + 4 = 6
3. 4 + 4 - 4 ÷ 4 = 7
4. 4 + 4 + 4 - 4 = 8
5. 4 × 4 + 4 + 4 = 24
6. 4 × (4 + 4) - 4 = 28
7. 4 × 4 + 4 × 4 = 32
8. 4 × (4 + 4 + 4) = 48

All use exactly four 4s and standard operations.

Double-check #2: (4 + 4) ÷ 4 + 4 = 8 ÷ 4 + 4 = 2 + 4 = 6 ✔
#3: 4 + 4 - (4 ÷ 4) = 8 - 1 = 7 ✔
#6: 4 × (4 + 4) - 4 = 4×8 - 4 = 32 - 4 = 28 ✔
#8: 4 × (4 + 4 + 4) = 4 × 12 = 48 ✔

All correct.

Final Answer:

4 4 4 4 = 3 → (4 + 4 + 4) ÷ 4
4 4 4 4 = 6 → (4 + 4) ÷ 4 + 4
4 4 4 4 = 7 → 4 + 4 - 4 ÷ 4
4 4 4 4 = 8 → 4 + 4 + 4 - 4
4 4 4 4 = 24 → 4 × 4 + 4 + 4
4 4 4 4 = 28 → 4 × (4 + 4) - 4
4 4 4 4 = 32 → 4 × 4 + 4 × 4
4 4 4 4 = 48 → 4 × (4 + 4 + 4)