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It was dark and cold in the land of Nemeria. A fellowship of heroes traversed a bridge in a straight line, one after another. Below them, only an abyss. They could hear the howling of strange creatures never seen by humans eyes. But they finally got to the other side of the bridge in safety. Their journey went on.

Below there were six Creatures from the Deep watching the heroes. One of them was their chief. He said:

The Abyss Creature Chief: "There could be humans, elves, dwarves, orcs and even halflings among this group of insolent folks. Were you able to tell which one was which?"

Creature from the Deep 1: "Yes, Chief! First there was a yummy halfling, then a filfhy orc, then a dwarf, a human, another dwarf, a detestable elf, another human and two dwarves." The Abyss Creature Chief: "You got six right guesses, but only one of them in the right position."

Creature from the Deep 2: "I saw a dwarf leading the party, followed by an elf, a human and his halfling slave, two young dwarves, another human and his halfling slave, and finally an orc prisoner." The Abyss Creature Chief: "You also got six right guesses, but two of them in the right position."

Creature from the Deep 3: "No, the leader was an ugly orc, then a halfling, an elf, another halfling, a dwarf, two female humans, another ugly orc and lastly a male human." The Abyss Creature Chief: "Better! You also got six right guesses, but half of them in the right position."

Creature from the Deep 4: "You are all blind! There were two orc leaders, then a halfling, another orc, and two dwarves followed by three pitiful humans." The Abyss Creature Chief: "You are no better than the others. Six right guesses, but again, only half of them in the right position."

Creature from the Deep 5: "I saw what I saw: the leader was a dwarf, followed by a strong orc, then two shiny elves, three tiny halflings, another elf and an orc in the last position." The Abyss Creature Chief: "Finally we have a winner. You got only four guesses right, but all of them were correct."

Then the Creatures from the Deep asked their master: "Chief, what did you see? What was the group consisted of?"

There is only one possibility that agrees with what the Chief saw. Please ignore any description or gender of the heroes, tell us just the sequence of species among humans, elves, dwarves, orcs and halflings.

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The Abyss Creature Chief said:

I saw a muscly leader dwarf, followed by another yummy dwarf, then a skinny elf, followed by another sickly looking elf, then a mountain of a human and his halfling slave, followed by two fierce looking female humans and finally another human warrior.

First I determined what the party consists of

Because creature 2 only differs from creature 1 by one less dwarf and one more halfling, this means that there cannot be more than 3 dwarfs and more than 1 halfling. If there were 4 dwarfs and 2 halflings then creature 3 could never have 6 correct guesses. Creature 5 has four correct guesses, if it guessed 1 of each of elf, dwarf, orc and halfling then the statements are inconsistent, because from creature 4 there would have to be at least 3 humans, but then creature 3 would have 7 correct guesses. There needs to be at least one dwarf, because creature 1 saw only 5 other people besides dwarfs. So for creature 5 to only have 4 correct guesses, the party has to be missing either elves, orcs or halflings. You can't have 3 elves and no orcs or halflings because then creature 4 would only have 5 correct guesses.
You can only have at most one halfling. If you do have one halfling, then for statements to work out you can't have any orcs. If you don't have any elves instead, then from creature 4's statement you will need to have 3 of humans or dwarfs. But from creature 3's statement, you need at least 2 humans and from creature 2's statement you need at least 2 dwarfs. So that doesn't work. The party will then have 4 humans, 2 elves, 2 dwarfs and 1 halfling.
If the party has no halflings, then the only way this works out is if there is only one orc. If the party has 2 orcs instead, then there can only be one elf. From creature 1 there can only be 2 dwarfs, and from creature 3 there can only be 2 humans and from creature 4 there can only be 2 orcs, but then there are only 2+1+2+2=7 people, but there were definitely 9 so that's out. So this will also result in 4 humans, 2 elves, 2 dwarfs and now 1 orc.

Now that the party is determined the only way I could see how to approach this is try to assert one position as correct and see if it works out.

First of all, we know the leader is a dwarf as creature 5 only saw one dwarf, so that has to be in the right place. Creature 3 only saw one elf, I assumed that that elf is out of position. Since creature 5 saw 3 elves, then the other two elves must be in position. Going through the cascade I got an error, so this means my assumption is wrong and one of the elves is in 3rd place. Then I tried both of the orcs - in the second and ninth place, but that didn't work out, so I know there are no orcs and just one halfling. Then I tried a dwarf in fifth and sixth place, that didn't work either. From creature 4 we know it got 3 places right. The only 3 places left from its statement is 3 humans in the last three places. Trying that out worked for all segments, so that's the correct answer.

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  • $\begingroup$ Congratulations, that is the right answer! Just out of curiosity, how difficult do you rate this problem? $\endgroup$ – Chaotic Mar 19 at 15:05
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    $\begingroup$ @Chaotic Well it definitely wasn't easy! Took me quite a bit of time to figure it out. I would rate it "hard". If you want a scale, 9/10 -- I want to leave some room for problems that I wouldn't even attempt, lol. $\endgroup$ – Amorydai Mar 19 at 15:50

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