On November 19th 2006, I set out with a friend to buy a Wii on launch day. After futilely showing up at about five stores, we took a chance at this small electronic boutique with ten people waiting outside. After getting into line at eleventh place, I was hearing murmurs of this place only having ten Wiis. We decided to wait the hour and a half and hope for an extra Wii. Five minutes to 11:00 am, this girl that was second in line with her boyfriend decided she was hungry and went to get a bite. Much to my surprise, when the guy came out of the store to tag who would get a Wii, she wasn’t there and I got the tenth and last Wii they had.
Since then, I rarely play games on it. I finished Twilight Princess, perfected my power serve in Wii Sports Tennis, and made my share of Miis. Though, this will change a bit when World of Goo releases. Recently, after browsing the Check Mii Out Channel, I started thinking: How many different Mii designs are possible? I started counting the options, did the math, and here are the results.
Options
| Attribute | Options | |
|---|---|---|
| 1 | Genders | 2 |
| 2 | Clothing Colors | 12 |
| 3 | Heights | 10 |
| 4 | Weights | 10 |
| 5 | Face Shapes | 8 |
| 6 | Makeup Types | 12 |
| 7 | Skin Colors | 6 |
| 8 | Hair Styles | 72 |
| 9 | Hair Parts | 2 |
| 10 | Hair Colors | 8 |
| 11 | Eyebrows | 24 |
| 12 | Eyebrow Colors | 8 |
| 13 | Eyebrow Vertical Steps | 16 |
| 14 | Eyebrow Size Steps | 9 |
| 15 | Eyebrow Rotation Steps | 12 |
| 16 | Eyebrow Horizontal Steps | 13 |
| 17 | Eye Types | 42 |
| 18 | Eye Colors | 6 |
| 19 | Eye Vertical Steps | 19 |
| 20 | Eye Size Steps | 8 |
| 21 | Eye Rotation Steps | 8 |
| 22 | Eye Horizontal Steps | 13 |
| 23 | Noses | 12 |
| 24 | Nose Vertical Steps | 19 |
| 25 | Nose Sizes | 9 |
| 26 | Lips | 24 |
| 27 | Lips Colors | 3 |
| 28 | Lips Vertical Steps | 19 |
| 29 | Lips Sizes | 9 |
| 30 | Glasses | 9 |
| 31 | Glasses Colors | 6 |
| 32 | Glasses Vertical Steps | 21 |
| 33 | Glasses Sizes | 8 |
| 34 | Mustaches | 4 |
| 35 | Mustache Colors | 8 |
| 36 | Mustache Vertical Steps | 17 |
| 37 | Mustache Sizes | 9 |
| 38 | Moles | 2 |
| 39 | Mole Vertical Steps | 31 |
| 40 | Mole Sizes | 9 |
| 41 | Mole Horizontal Steps | 17 |
| 42 | Goatee Types | 4 |
| 43 | Goatee Colors | 8 |
| Total | 568 |
Exceptions
- 1 hair style (bald) has no color or part
- 49 hair styles have no part
- 1 eyebrow style(none) has no color, vertical step, size, rotation or horizontal step
- 7 eye types have no color
- 17 lips have no color
- 1 glasses type (none) has no color, vertical step, or size
- 1 mustache type (none) has no color, vertical step, or size
- 1 mole (none) has no vertical step, size, or horizontal step
- 1 goatee type (none) has no color
Combinations
To determine the number of distinct combinations I used the formula: 568! / (43! * (568-43)!)
Result
Using Wolfram Alpha to solve 568! / (43! * (568-43)!), we can see that there are 88 vigintillion, 613 novemdecillion, 583 octodecillion, 674 septendecillion, 758 sexdecillion, 947 quindecillion, 813 quattuordecillion, 475 tredecillion, 143 duodecillion, 744 undecillion, 24 decillion, 970 nonillion, 165 octillion, 692 septillion, 788 sextillion, 754 quintillion, 421 quadrillion, 531 trillion, 161 billion, 395 million, 650 thousand and 32 Mii Combinations.