What are the roman numerals between 1 to 50 which are not repeated ?
The correct answer and explanation is:
Correct Answer:
The Roman numerals between 1 to 50 that are not repeated are:
I, V, X, L, VI, VII, VIII, IX, XI, XV, XVI, XIX, XL, XLV, XLVI, XLIX
These numerals contain no repeated characters (no letter appears more than once).
Explanation:
Roman numerals are based on a combination of letters from the Latin alphabet. The primary symbols used are:
- I = 1
- V = 5
- X = 10
- L = 50
In constructing numbers, these letters are combined based on specific rules. Some involve adding values (e.g., VI = 5 + 1 = 6), and some involve subtracting values (e.g., IV = 5 – 1 = 4).
A Roman numeral is said to be “not repeated” if it does not use any character more than once. For example, the numeral II for 2 repeats the letter I, so it is not considered. But VI (6) uses V and I only once each, so it qualifies.
To find all such numerals from 1 to 50:
- Convert numbers from 1 to 50 into Roman numerals.
- Check if any letter appears more than once in each numeral.
- Select only those numerals where no letter is repeated.
Examples:
- I (1) uses I once.
- V (5) uses V once.
- VI (6) uses V and I once each.
- VIII (8) is not included because I appears three times.
- XX (20) is excluded because X is repeated.
- XL (40) is valid because X and L appear only once.
- XLIX (49) is valid because it uses X, L, I and V once each.
This method helps identify Roman numerals with unique characters, useful in educational settings, design work, or puzzles where repetition needs to be avoided.