Magic Numbers

很多文件格式都是以一个 Magic number 开始，例如 Java 编译后的字节码文件就是以 CAFEBABE 开头。Wikipedia 上还有一个 表，里面放了很多好玩的 magic number，例如 DEADBEEF （还有个音乐播放器叫这个名字）和 FEE1DEAD （linux 的 reboot syscall 中用到）。于是我就心血来潮，能不能整出类似的看起来像英文词组的 magic numbers 。

首先我们要限定一下范围：

  • 字符串长度限制为恰好为 8；
  • 能被拆成一个或多个英文单词。由于英文单词也没有准确的定义，和之前一样，我这里采用 unix 自带的字典。
  • 字符集允许 0-9A-F 。这字符集有点小，但是我们可以整一些字符的 alias
    • O => o
    • I => 1
    • L => 1。由于 I 和 L 都映射到了 1，所以我限制这两个字母不能同时出现
    • ATE => 8
    • 或许可以允许 S => 5？
    • 或许可以允许 K => C？
    • 或许可以允许 G => 9？
  • 每个拆分的单词长度在 3-8 之间。

事实上，我们可以先看一下那些单词可以在这些规则下表示出来。

跑了之后发现里面这样 unix 自带字典 /usr/share/dict/words 太大，23w 个词，太多词我不认识了……为了解决这个问题我决定按照词频排序，于是我找到了 wordfreq 这个 repo。虽然他因为 AI generated content 污染决定不更新词频统计了，但是我们还是相信它吧。于是我们把词限定在这两个交集：可以去除一些人名地名、过去分词、专有名词，还可以按照词频排序。

我先看看有那些词替换之后直接就是 8 个字符。这种词总共只有 8 个：

ACC01ADE => accolade
F01DAB1E => foldable
CA11AB1E => callable
DEADFA11 => deadfall
CAB00D1E => caboodle
D011FACE => dollface
C0C0B010 => cocobolo
C0CC1D1A => coccidia

但是如果你允许 S => 5 的话，small list 都有一些了：

BA5EBA11 => baseball
DECEA5ED => deceased
A55E55ED => assessed
C01055A1 => colossal
5E1F1E55 => selfless
D15EA5ED => diseased
BA5E1E55 => baseless
5CAFF01D => scaffold

剩下要组词的话，由于限制 8 个字符，所以只能是一个 3-5 字符的词 + 一个 5-3 字符的词。这样的词总共只有 300 个左右，列表如下：

3-5 字符的词

A11      => all
D1D      => did
0FF      => off
01D      => old
FEE1     => feel
BAD      => bad
CA11     => call
FACE     => face
AB1E     => able
10CA1    => local
F00D     => food
1DEA     => idea
DEA1     => deal
1EAD     => lead
DEAD     => dead
ADDED    => added
C001     => cool
FA11     => fall
1ED      => led
B100D    => blood
ADD      => add
C0DE     => code
BED      => bed
D1E      => die
BA11     => ball
C01D     => cold
1CE      => ice
DAD      => dad
CE11     => cell
FE11     => fell
A1D      => aid
1EE      => lee
FEED     => feed
DEB8     => debate
B0B      => bob
BE11     => bell
10AD     => load
CAB1E    => cable
FED      => fed
FEE      => fee
C0A1     => coal
FACED    => faced
AC1D     => acid
1ABE1    => label
1AB      => lab
0DD      => odd
B1D      => bid
D0C      => doc
F100D    => flood
BEEF     => beef
F001     => fool
B01D     => bold
1EAF     => leaf
B1ADE    => blade
C01E     => cole
ACE      => ace
BABE     => babe
BEE      => bee
F01D     => fold
D011     => doll
F1ED     => fled
CA1      => cal
DEAF     => deaf
DA1E     => dale
CAB      => cab
C01      => col
10C8     => locate
B00      => boo
1AD      => lad
C0D      => cod
FADE     => fade
DEE      => dee
D0E      => doe
BA1D     => bald
1ACE     => lace
F1EE     => flee
BE11E    => belle
D1CE     => dice
DEED     => deed
C01A     => cola
FADED    => faded
B1EED    => bleed
CA1F     => calf
A1DE     => aide
A1E      => ale
DE11     => dell
F0CA1    => focal
A1EC     => alec
E1F      => elf
C0CA     => coca
C0C0A    => cocoa
BA1E     => bale
B10C     => bloc
AB1DE    => abide
BABA     => baba
BAE      => bae
C1AD     => clad
1EA      => lea
AD0BE    => adobe
A1A      => ala
F0E      => foe
C0C0     => coco
10AF     => loaf
1CED     => iced
BEAD     => bead
E11E     => elle
BE1      => bel
F1EA     => flea
B00B     => boob
CAD      => cad
F1FE     => fife
D0DD     => dodd
0B1      => obi
D0D      => dod
F00      => foo
A1BA     => alba
D01E     => dole
ABA      => aba
DAB      => dab
1AC      => lac
0DE      => ode
C00      => coo
10BE     => lobe
100      => loo
CE110    => cello
1ACED    => laced
DAE      => dae
F1DE     => fide
FAD      => fad
DA1      => dal
DEB      => deb
EE1      => eel
B1ED     => bled
10C0     => loco
AD0      => ado
B0A      => boa
FE1      => fei
DADE     => dade
FAB1E    => fable
C0E      => coe
1DE      => ide
AB0DE    => abode
BA1      => bal
A1F      => alf
BAC      => bac
F0B      => fob
DADA     => dada
0DA      => oda
A1FA     => alfa
B10B     => blob
A10E     => aloe
D10DE    => diode
B0D      => bod
CABA1    => cabal
C0B      => cob
EBB      => ebb
B0DE     => bode
B0B0     => bobo
DECA1    => decal
FECA1    => fecal

要组词的话其实挺简单的，因为这里面有足够的动词名词形容词：

  • 动词： 
    FEE1 => feel
CA11 => call
DEA1 => deal
FA11 => fall
FEED => feed
  • 名词 
    FACE => face
FOOD => food
1DEA => idea
1CE  =>  ice
BEEF => beef
  • 形容词 
    A11  =>  all
01D  =>  old
BAD  =>  bad
C001 => cool
DEAD => dead

如果只看 wordfreq small list 里的，那更少，只有 160 个。我自己稍微组了一些词：

FEE1BAAD => feel bad       这个其实不太可行，因为我用的 BAAD，也可以考虑 FEE15BAD
A10EFOOD => aloe food
DEB81DEA => debate idea
BADCAB1E => bad cable
ADD1ABE1 => add label
DEADF001 => dead fool      差一点变成了 deadpool
1EAFFA11 => leaf fall      让我想起了 e.e. cummings 的诗 l(a

如果我们不允许任何 alias，只用 A-F 来组词，也是能组出一些的：

DEADBEEF => dead beef    经典
FEEDBABE => feed babe    张嘴，啊～
FADEDDAD => faded dad    我去买个橘子？

我挑了一些词：

部分只包含 A-F 的词

BAD      => bad
FACE     => face
DEAD     => dead
ADDED    => added
ADD      => add
BED      => bed
DAD      => dad
FEED     => feed
DECADE   => decade
FED      => fed
FEE      => fee
FACED    => faced
BEEF     => beef
ACE      => ace
BABE     => babe
BEE      => bee
DEAF     => deaf
CAB      => cab
FADE     => fade
DEED     => deed
FADED    => faded
BEAD     => bead
FACADE   => facade
DAB      => dab
FAD      => fad
BEADED   => beaded
EBB      => ebb

可以看到长度为 5 的词很少，所以 3+5 和 5+3 这种搭配不好组词，只能 4+4 的组。

代码不长我就直接放这里了：

代码

import wordfreq
from pathlib import Path


def transform(x):
    result = x.upper()
    for c in x:
        if not c.isalpha():
            return None
    if "I" in result and "L" in result:
        return None

    # if result.endswith("ATE"):
    #     result = result[:-3] + "8"
    # result = result.replace("L", "1")
    # result = result.replace("O", "0")
    # result = result.replace("I", "1")
    # result = result.replace("S", "5")

    for c in result:
        if not c.isdigit() and c > "F":
            return None

    return result


dictionary = set(Path("/usr/share/dict/words").read_text().splitlines())


words = {}
for w in wordfreq.iter_wordlist("en", wordlist="small"):
    if w not in dictionary:
        continue
    w2 = transform(w)
    if w2 and w2 not in words and 3 <= len(w2) <= 8:
        words[w2] = w

for w2, w in words.items():
    print(f"{w:12} => {w2:12}")