How To Generate Any Number Using Four 4s? By Hemanth Street, 57% OFF - Free Printable

The image you've provided contains a sequence of mathematical expressions, each forming a number from 0 to 10 using only the digit 4 and basic arithmetic operations (addition, subtraction, multiplication, division, parentheses, and square roots). The goal is likely to verify or understand how each number is constructed using exactly four 4s (or variations thereof), which is a classic "Four Fours" puzzle.

Let’s go through each line step by step, verify correctness, and explain the logic.

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✔ 0 = 4 − 4 + 4 − 4

- Calculation:
$ 4 - 4 = 0 $, then $ 0 + 4 = 4 $, then $ 4 - 4 = 0 $
- Result: 0 ✔

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✔ 1 = 4 ÷ 4 + 4 − 4

- $ 4 ÷ 4 = 1 $
- $ 1 + 4 = 5 $
- $ 5 - 4 = 1 $
- Result: 1 ✔

> Alternatively: $ \frac{4}{4} + 4 - 4 = 1 + 0 = 1 $

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✔ 2 = 4 ÷ 4 + 4 ÷ 4

- $ 4 ÷ 4 = 1 $
- $ 1 + 1 = 2 $
- Result: 2 ✔

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✔ 3 = (4 + 4 + 4) ÷ 4

- $ 4 + 4 + 4 = 12 $
- $ 12 ÷ 4 = 3 $
- Result: 3 ✔

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✔ 4 = 4 × (4 − 4) + 4

- $ 4 - 4 = 0 $
- $ 4 × 0 = 0 $
- $ 0 + 4 = 4 $
- Result: 4 ✔

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✔ 5 = (4 × 4 + 4) ÷ 4

- $ 4 × 4 = 16 $
- $ 16 + 4 = 20 $
- $ 20 ÷ 4 = 5 $
- Result: 5 ✔

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✔ 6 = 4 × 4 + 4.4 = 4 + (4 + 4) ÷ 4

Wait — this one has two expressions:

#### First version:
6 = 4 × 4 + 4.4
- But $ 4 × 4 = 16 $, $ 16 + 4.4 = 20.4 $ → ✘ Not 6

This seems incorrect.

But then it says:
= 4 + (4 + 4) ÷ 4

Let's check that:
- $ 4 + 4 = 8 $
- $ 8 ÷ 4 = 2 $
- $ 4 + 2 = 6 $ ✔

So the correct expression is:
> 6 = 4 + (4 + 4) ÷ 4

The first part “4 × 4 + 4.4” is wrong — probably a typo.

✔ Corrected:
6 = 4 + (4 + 4) ÷ 4

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✔ 7 = 4 + 4 − (4 ÷ 4)

- $ 4 ÷ 4 = 1 $
- $ 4 + 4 = 8 $
- $ 8 - 1 = 7 $
- Result: 7 ✔

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✔ 8 = 4 + 4.4 − .4 = 4 + 4 + 4 − 4

Two versions given:

#### First:
8 = 4 + 4.4 − 0.4
- $ 4 + 4.4 = 8.4 $
- $ 8.4 - 0.4 = 8 $ ✔

#### Second:
8 = 4 + 4 + 4 − 4
- $ 4 + 4 = 8 $, $ 8 + 4 = 12 $, $ 12 - 4 = 8 $ ✔

Both are valid, though the second uses four 4s, the first uses decimals.

Note: Using 4.4 and .4 implies concatenation or decimal points, which are allowed in some versions of the Four Fours puzzle.

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✔ 9 = 4 + 4 + 4 ÷ 4

- $ 4 ÷ 4 = 1 $
- $ 4 + 4 = 8 $
- $ 8 + 1 = 9 $
- Result: 9 ✔

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✔ 10 = 4 + √4 + √4 + √4

- $ \sqrt{4} = 2 $
- So: $ 4 + 2 + 2 + 2 = 10 $
- Result: 10 ✔

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## ✔ Summary & Observations:

All numbers from 0 to 10 are expressed using only the digit 4 and standard operations.

However, some expressions use decimals like 4.4 or .4, which may be considered concatenation (not strictly using four 4s), but are commonly accepted in extended versions of the puzzle.

Also, note that √4 = 2 is used — this is acceptable since √4 is derived from 4.

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Final Answer:

✔ All equations from 0 to 10 are correct except for the expression for 6.

> Incorrect: `6 = 4 × 4 + 4.4` → This equals 20.4, not 6.

> Correct version:
> 6 = 4 + (4 + 4) ÷ 4

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✔ Corrected Full List:

| Number | Expression |
|--------|------------|
| 0 | 4 − 4 + 4 − 4 |
| 1 | 4 ÷ 4 + 4 − 4 |
| 2 | 4 ÷ 4 + 4 ÷ 4 |
| 3 | (4 + 4 + 4) ÷ 4 |
| 4 | 4 × (4 − 4) + 4 |
| 5 | (4 × 4 + 4) ÷ 4 |
| 6 | 4 + (4 + 4) ÷ 4 |
| 7 | 4 + 4 − (4 ÷ 4) |
| 8 | 4 + 4 + 4 − 4 or 4 + 4.4 − 0.4 |
| 9 | 4 + 4 + 4 ÷ 4 |
| 10 | 4 + √4 + √4 + √4 |

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🎯 Conclusion:

The task was to express numbers 0–10 using only the digit 4 and standard operations. Most expressions are correct. Only the expression for 6 had an error, which has been corrected.

Let me know if you'd like to extend this to higher numbers (like 11–20) or restrict to exactly four 4s without decimals!