Solution:
1. Consider possible operations and placement of parentheses:
- Try inserting operations:
* Possible operation: (6 * 6) * (6 + 6) - 6
2. Simplify and verify:
* Calculate first part: 6 * 6 = 36
* Calculate second part inside parentheses: 6 + 6 = 12
* Compute their product: 36 * 12 = 432
* Subtract 6: 432 - 6 = 426
3. Trying another arrangement:
- Use the pattern (6 \cdot 6) \cdot 6 + 6 \cdot 6 to match 630:
* Compute inside parentheses: 6 \cdot 6 = 36
* Calculate the first term: 36 \cdot 6 = 216
* Calculate the second term: 6 \cdot 6 = 36
* Their sum should be:
* Recalculate (6\cdot6)\cdot5 \cdot 6 = 630
4. Alternatively:
* Apply trial in 666 - 6^2 - 6 becomes 666 - 36= 630
5. Correct configuration:
* Insert operations to get number: (6 \cdot 6 \cdot 6) + (6 \cdot 6)
* Verify computation: 6 \cdot 6 \cdot 6=216 and 6\cdot 6=36
* Sum is: 216 + 36 = 252
5. Recheck for:
* Correct operations till 666 -6^{2}- 6
* Actual configuration: 666 - 36= 630
3. Conclude:
* Final correct arrangement and expression : 666 - 36 = 630