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Eldrow

专题
Programming
难度
L9

题目详情

日常解谜游戏 Wordle 风靡全球！Wordle玩家每天试图用尽可能少的猜测次数来找出神秘的五个字母单词，每次猜测都会返回以下关于其字母的信息：

  • 在神秘单词中且位置完全正确（这些字母变绿），

  • 在神秘单词中，但不在猜测的位置上，且尚未被绿色或黄色字母说明，计算重复次数（这些字母变黄），或者

  • 根本不在神秘单词中（这些字母变灰）。

标记按此特定顺序发生。首先，所有放置正确的字母都被标记为绿色。然后，从剩下的字母中，从左到右，所有存在于神秘单词中但尚未被绿色或黄色说明的字母都被标记为黄色。其余的字母被标记为灰色。如果神秘单词是 ROVER，猜测 ERROR 将被标记为

ERRO****R

在*困难模式（hard-mode）*下运行时，随后的每次猜测都必须满足先前猜测留下的所有线索，即，在所有先前猜测的响应为条件的情况下，每次猜测都必须有成为神秘单词的可能性[1](#fn:1)。例如，如果 TIGER 是神秘单词，而玩家的第一次猜测是 TRACK，它将被着色为

TRACK

并且任何未来的猜测都不能是

  • DIRTY，因为神秘单词以 T 开头

  • TROMP，因为神秘单词的第二个字母不是 R

  • TARDY，因为神秘单词不包含 A

  • TEPID，因为神秘单词必须包含 R。

还有许多其他不合格的未来猜测，但例如 TOWER 将被允许。

我们正在玩 Eldrow，这是一个寻找最长可能的困难模式猜测链的游戏（我们忽略了 Wordle 中 6 次猜测的限制）。从[2](#fn:2) 此列表 中选择目标单词和困难模式猜测序列（剧透警告：这是 Wordle 神秘单词列表的按字母顺序排列的副本，通过检查网站源代码找到）。

你能找到的最长困难模式猜测序列是什么[3](#fn:3)？将您的答案作为从上面链接的列表中选择的逗号分隔单词列表提交，按猜测顺序排列，最后一个单词是选择的目标单词。例如，“TRACK,TOWER,TIGER”将是一个略显平庸的提交（而“TRACK,TROMP,TIGER”将不符合条件）。我们将在此页面上保留最长合格提交的排行榜！

1. \$1

2. \$1

3. \$1

The daily puzzle game Wordle has taken the world by storm! Wordlers try to track down the mystery five-letter word in as few guesses as possible each day, with each guess returning the information of whether its letters are:

  • in the exact position they appear in the mystery word (these letters turn green),
  • in the mystery word but NOT in the position guessed and NOT already accounted for by green or yellow letters, counting duplicity (these letters turn yellow), or
  • not in the mystery word at all (these letters turn gray).

The marking happens in this specific order. First all correctly placed letters are marked green. Then of the remaining letters, from left to right, all letters that exist in the mystery word but haven’t been accounted for by greens or yellows so far are marked yellow. The remaining letters are marked gray. If the mystery word is ROVER, the guess of ERROR would be marked

ERROR

When operating in hard-mode, every subsequent guess has to satisfy all clues left by previous guesses, i.e., each guess has to have a possibility of being the mystery word conditional on the responses of all previous guesses1. For example, if TIGER is the mystery word, and a player’s first guess is TRACK, it would be colored

TRACK

and any future guess couldn’t be

  • DIRTY, because the mystery word starts with T
  • TROMP, because the mystery word’s second letter isn’t R
  • TARDY, because the mystery word doesn’t contain an A
  • TEPID, because the mystery word must contain an R.

There are many other disqualified future guesses, but TOWER for example would be allowed.

We are playing Eldrow, the game of searching for the longest possible chain of hard-mode guesses (we ignore the limit of 6 guesses in Wordle). Choose the target word and sequence of hard-mode guesses from2 this list (SPOILER ALERT: this is an alphabetized copy of the list of Wordle mystery words, found from inspection of the website’s source code).

What is the longest hard-mode guess sequence you can find3? Submit your answer as a comma-separated list of words from the list linked above, in the order guessed, with the final word being the chosen target word. For example, “TRACK,TOWER,TIGER” would be a somewhat underwhelming submission (and “TRACK,TROMP,TIGER” would not qualify). We will keep a leaderboard of the longest qualifying submissions on this page!

  1. In the actual Wordle game, this isn’t precisely true. The exact requirement is that, in every future guess, all green letters discovered so far appear in the position discovered and all yellow letters discovered so far continue to appear in future guesses. So in the example above with TIGER as the mystery word, the sequence

    TRACK

    TROMP

    is allowed, even though the player knows that the R can’t be in the second position after the first guess because it would’ve been colored green in the first row. We will use our definition of hard-mode: every guess has to be a potential winner given all the information gathered so far (so by the above logic this sequence would NOT be allowed). ↩

  2. If you’d prefer to solve by hand without testing each word against this list, your can still submit but your leaderboard entry may have an asterisk. ↩

  3. Note there is a fairly straightforward proof that an (unachievable) upper bound on the length of an Eldrow sequence is 26 words. If your process is generating longer sequences, please recheck the rules. ↩

解析

本月的谜题吸引了多种不同的解决方法，一些使用了代码，而另一些则使用了对单词列表的手动搜索。迄今为止发现的最长解长度为 16，这个长度的第一个提交是

GAZER,INNER,QUEER,ODDER,BOXER,FOYER,HOVER,JOKER, WOOER,LOWER,MOWER,POWER,ROWER,SOWER,TOWER,COWER

由解谜者 Andrew Sultana 提交，他指出使用了字母表中的每个字母！

解谜者 Karl Mahlburg 想出了一个类似的序列，并解释了为什么没有长度为 17 的 Eldrow 解（虽然承认这不是一个完全严格的证明）。本质上，每个单词都通过含有变灰的字母来向被消除的字母列表中添加字母，因此我们可以将搜索集中在被消除字母可能减少的序列部分。运行代码来搜索这些区域未能找到更长的序列。

干得好，解谜者们！我们当然对我们的 16 长度 Eldrow 序列感到满意，并好奇是否有某种神奇的 17 长度序列潜伏在那里……

恭喜本月的解谜者，按长度降序排列，平局由最早提交者打破。

Original Explanation

This month’s puzzle drew several different solution methods, some employing code and others using a hand search of the word list. The longest solutions so far discovered are length 16, the first submission of this length was

GAZER,INNER,QUEER,ODDER,BOXER,FOYER,HOVER,JOKER, WOOER,LOWER,MOWER,POWER,ROWER,SOWER,TOWER,COWER

submitted by solver Andrew Sultana, who noted that every letter of the alphabet is used!

Solver Karl Mahlburg came up with a similar sequence, and also an explanation for why there wasn’t a length 17 Eldrow solution (while admitting it wasn’t a completely rigorous proof). Essentially, each word adds letters to the list of eliminated letters by having grayed out letters, and so we can focus our search on the parts of the sequence where eliminated letters could be reduced. Running code to search these areas failed to find a longer sequence.

Nice work solvers! We are certainly happy with our 16-length Eldrow sequences, and curious if some magical 17-length sequence is lurking out there…

Congrats to this month’s solvers, ordered by descending length, with ties broken by who submitted earliest.