Which of the following Roman numerals are not valid? State the reason for your answer in each case.
ICCVI

Answer

To determine whether the Roman numeral "ICCVI" is valid, let's analyze it step by step.

### Step 1: Identify the Roman Numerals
The Roman numeral "ICCVI" consists of the following symbols:
- I = 1
- C = 100
- V = 5

### Step 2: Analyze the Order of the Symbols
In Roman numerals, certain rules govern the order of symbols:
- A smaller numeral can precede a larger numeral to indicate subtraction (e.g., IV = 4).
- A smaller numeral cannot precede a larger numeral if it is not one of the allowed subtractions (e.g., I cannot precede C).

### Step 3: Check the Validity of "ICCVI"
In "ICCVI":
- The first 'I' is followed by 'C', which is valid since 'I' (1) can precede 'C' (100) for subtraction.
- The second 'C' is also followed by 'C', which is valid as 'C' can repeat.
- However, the next 'C' is followed by 'V'. According to Roman numeral rules, 'I' should not precede 'C' in this context because 'I' is not allowed to subtract from 'C'.

### Step 4: Conclusion
Since 'I' is incorrectly placed before 'C' in the numeral "ICCVI", it makes this Roman numeral invalid.

### Step 5: Correcting the Roman Numeral
To correct the numeral, we should rearrange it to follow the rules of Roman numerals. A valid arrangement would be "CCVII":
- C (100) + C (100) + V (5) + I (1) + I (1) = 207.

### Final Answer
The Roman numeral "ICCVI" is not valid because 'I' cannot precede 'C' in this context. A valid form would be "CCVII".

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