Super Bowl LI
Something about roman numerals, inspired by Super Bowl LI
Why
Cheer out for the Patriots and Falcons fans! I am excited about this year's super bowl. Will Tom Brady win his FIFTHS or Matt Ryan finish strong for his amazing season?
When I was watching the conference finals on Sunday afternoon, my wife asked "why your name is with super bowl". For a second I was like, with a Nick Young face, "what?" Then I realized she was referring to "SB LI" and replied "that's roman 51".
Why Cont'd
Answering why NFL uses roman numerals is not the main concern of this post. Clearly roman numerals should be easy to understand in early days but they may get complex later. For example, what does XXXVIII stand for or what is 39 in roman numeral?
If you can tell within a blink. TL;DR
Roman Numerals
Let's begin with a chart for roman numerals
| Roman Numeral | Integer |
|---|---|
I | 1 |
V | 5 |
X | 10 |
L | 50 |
C | 100 |
D | 500 |
M | 1000 |
Alrighty. This makes sense. How about the values in between?
How to Read
Let's begin with the simple cases.
| Roman Numeral | Integer |
|---|---|
I | 1 |
II | 2 |
III | 3 |
IV | 4 |
V | 5 |
VI | 6 |
VII | 7 |
VIII | 8 |
IX | 9 |
X | 10 |
Rules:
-
A roman numeral is written left to right.
-
Values are added left to right if former letter is no smaller than the latter one.
See II (2), VII (7)
- If the former is smaller, discard the previous added value and subtract the former from then the latter one.
See IV (4), IX (9)
To summarize, we simply keep adding the value of a roman letter till we see a bigger letter. If we encounter a bigger letter, adjust the value by subtracting 2 times of the previous value from the latter.
For example:
| Roman Numeral | Action |
|---|---|
I | +1 |
II | +1, +1 |
III | +1, +1, +1 |
IV | +1, +5, -1 x 2 |
V | +5 |
VII | +5, +1, +1 |
VIII | +5, +1, +1, +1 |
IX | +1, +10, -1 x 2 |
X | +10 |
Let's check another value XLIX (49)
XLIX = +10, +50, -10 x 2, +1, +10, -1 x 2 = 49
Looking good! But the rules seem to work only if the given roman numeral is legit.
We can also conclude that the biggest roman numeral constructed by the aforementioned letters is 3999 as in MMMCMXCIX
How to Write
Given a number from 1 to 3999, constructing a legit roman numeral requires:
-
selecting the maximum roman letter no larger than the number
-
subtracting the value from the number
-
repeat step 1 until number is 0
Let's take 3998 as an example:
| number | roman numeral | remaining |
|---|---|---|
| 3998 | M | 2998 |
| 2998 | M | 1998 |
| 1998 | M | 998 |
| 998 | D | 498 |
| 498 | C | 398 |
| 398 | C | 298 |
| 298 | C | 198 |
| 198 | C | 98 |
We know DCCCC is not a legit roman numeral, which should be written as CM.
| number | roman letter | remaining |
|---|---|---|
| 998 | CM | 98 |
Similarly,
| number | roman letter | remaining |
|---|---|---|
| 98 | XC | 8 |
And finally,
| number | roman letter | remaining |
|---|---|---|
| 8 | V | 3 |
| 3 | I | 2 |
| 2 | I | 1 |
| 1 | I | 0 |
Therefore, 3998 is MMMCMXCVIII.
Let's look at 4 as another example
| number | roman letter | remaining |
|---|---|---|
| 4 | I | 3 |
| 3 | I | 2 |
| 2 | I | 1 |
| 1 | I | 0 |
We know IIII is not a legit roman numeral, which should be written as IV.
Hmm... to speed up the conversion, we may include 9 x 10 ^ n and 4 x 10 ^ n patterns in the matching process.
Python Implementation
See my Python implementation (and test) at the following gist.
The End
Okay. XXXVIII is 38 and 39 is XXXIX
If you speak Chinese, you may also find "SB LI" hilarious.
Thanks for reading.