To solve the problem of determining how many match-sticks you require to arrange the number 2065 in Roman numerals, we'll break it down into smaller steps. First, we'll convert the number 2065 into its Roman numeral equivalent. Then, we'll count the number of match-sticks required for each Roman numeral symbol.
### Step 1: Convert 2065 to Roman Numerals
Roman numeral values are composed of the following symbols:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
We can break down 2065 as follows:
- 2000: 'MM'
- 60: 'LX'
- 5: 'V'
So, 2065 in Roman numerals is:
'MMLXV'
### Step 2: Determine the Number of Match-Sticks Needed
We need to know the number of match-sticks required to form each Roman numeral symbol. Let's assume we have the number of match-sticks for each of these characters:
- I: 1 match-stick
- V: 2 match-sticks
- X: 2 match-sticks
- L: 2 match-sticks
- C: 2 match-sticks
- D: 3 match-sticks
- M: 4 match-sticks
### Step 3: Calculate the Total Number of Match-Sticks
Now we'll count the match-sticks required for each symbol in 'MMLXV':
- 'M' (2000): Each 'M' needs 4 match-sticks. There are 2 'M's in 'MMLXV'.
[tex]\( 4 \times 2 = 8 \text{ match-sticks} \)[/tex]
- 'L' (50): Each 'L' needs 2 match-sticks.
[tex]\( 2 \times 1 = 2 \text{ match-sticks} \)[/tex]
- 'X' (10): Each 'X' needs 2 match-sticks.
[tex]\( 2 \times 1 = 2 \text{ match-sticks} \)[/tex]
- 'V' (5): Each 'V' needs 2 match-sticks.
[tex]\( 2 \times 1 = 2 \text{ match-sticks} \)[/tex]
Adding these up:
[tex]\[ 8 + 2 + 2 + 2 = 14 \][/tex]
Therefore, you require 14 match-sticks to arrange the number 2065 in Roman numerals.
