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This puzzle is part of the Puzzling StackExchange Advent Calendar 2021. The accepted answer to this question will be awarded a bounty worth 50 reputation.

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Santa had a conversation with Alice, Bob, Charlie, David, Eve and Frank. It was supposed to be all fun and games for the kids; telling him what they want for christmas. But Santa's dark motive was to evaluate which of these little rascals will get charcoal for christmas this year. I managed to get a peek at his naughty or nice list:

Alice: Nice
Bob: Naughty
Charlie: Nice
David: Nice
Eve: Naughty
Frank: Naughty

Below is a partial transcript of the conversations. Can you determine Santa's secret rule? He is a very fast thinker.

S: Ok kids, no naughty words please. Let's start with you, Alice. What do you want for christmas?

A: I'd like a real baby dragon!
S: Be realistic
A: Mom and Dad unindebted
S: What color do you want the dragon to be?
...
B: A quarter dollar.
S: That was close.
B: Maybe just a few sweets, please.
S: Forget it.
...
C: A Beverly Hills mansion and world domination
S: Sure!
...
D: Cultural commercialisation
S: Ho ho ho! You have so much positivity!
...
E: The answer to life, the universe and everything
S: Don't be so negative.
E: Some candy?
S: Too late.
...
F: Is this a bad joke, Santa? My father told me everything about you
S: Perhaps. You still got a chance, though. What is it that you want?
F: A trip to queenwood and some arsenobenzene.
S: Ok, nevermind. You're an extremely unbalanced young boy.

Note:

The rule only evaluates the words spoken by the corresponding kid. Punctuation and capitalization is not considered.


Hints:

"Positive", "Negative", "Unbalanced"
Apply to each letter, sum the results.

"Commercialisation" = 11
"Cultural" = 8
"Quarter" = 0
"on" = -3
"Queenwood" = -5
"Arsenobenzene" = -9

Convert each letter to A1Z26, then convert to [REDACTED].

The [REDACTED] of a letter consists of negative, neutral and or positive components.
amountOfPositive - amountOfNegative gives the word its score.

Among others, E, Q and N are risky letters.

Now it's your turn.

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    $\begingroup$ Incidentally Code Golf is doing an Advent event too, and we had a challenge with the same title... because Santa :D $\endgroup$
    – Bubbler
    Dec 7, 2021 at 10:10
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    $\begingroup$ Can Santa use this rule to assess children who would write using a non-roman alphabet (or even using anything other than the 26 character English alphabet)? For example, would he be able to evaluate an Arabic, Chinese or certain French words? $\endgroup$
    – Crimsonfox
    Dec 7, 2021 at 18:20
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    $\begingroup$ The rule could be simple. If the kids speak any word containing "p" or the word "some" then they are out. Of course, this is not in line with the hint that gives a value to each word. $\endgroup$
    – Florian F
    Dec 7, 2021 at 21:16
  • $\begingroup$ Given the latest hints, is this question missing the knowledge tag? $\endgroup$
    – hb20007
    Dec 8, 2021 at 14:07
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    $\begingroup$ @hb20007 Nope. "Elements" can be swapped with any synonym $\endgroup$ Dec 8, 2021 at 14:08

2 Answers 2

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I used the following assumptions:

Santa declares as naughty any child that expresses a naughty word.

In the case of Bob and Fred, it is the second sentence that has a naughty word.
In the case of Eve, she said a naughty word in the first sentence and Santa mentioned the negativity. The second sentence was OK, but it was too late.

The principle as explained in the hint is that each letter has a value and the sum of the values decides whether the word is naughty. If the sum is negative it is a naughty word.

And the solution is:

Take the following letter values:

N = -2, E,O,Q,W = -1, B,F,H,P,R,T,X,Z = 0, A,C,G,I,K,S,U,Y = +1, D,J,L,V = +2, M = +3

With these values we can review the dialogue:

A: I=1 d=2 like=3 a=1 real=2 baby=2 dragon=1
S: Be realistic. (so far so good, all positives)
A: Mom=5 and=1 Dad=5 unindebted=0
S: What color do you want the dragon to be? (OK, all words are positive)
...
B: A=1 quarter=0 dollar=6
S: That was close. (because quarter is 0, almost negative)
B: Maybe=4 just=4 a=1 few=-2 sweets=-1 please=2
S: Forget it. (a few negative word)
...
C: A=1 Beverly=3 Hills=6 mansion=1 and=1 world=2 domination=2
S: Sure! (selfish but all words are positive)
...
D: Cultural=8 commercialisation=11
S: Ho ho ho! You have so much positivity! (indeed, very positive words)
...
E: The=-1 answer=-2 to=-1 life=2 the=-1 universe=1 and=1 everything=1
S: Don't be so negative. (There are a few negative words)
E: Some=2 candy=3
S: Too late. (Would be OK, but it is too late.)
...
F: Is=2 this=2 a=1 bad=3 joke=1 Santa=1 My=4 father=0 told=3 me=2 everything=1 about=1 you=1
S: Perhaps. You still got a chance, though. What is it that you want? (so far no negative words)
F: A=1 trip=1 to=-1 queenwood=-5 and=1 some=2 arsenobenzene=-9
S: Ok, nevermind. You're an extremely unbalanced young boy. (Indeed, a few extremely negative words)

The reason for these values is as follows. The key word is "unbalanced".

The value of a letter is found as follows.

Convert each letter to its ordinal number: A=1, B=2, ... , Z=26.

Then consider that you want to weigh that many kilo on a 2-pane balance.

As in the classical puzzle, you will use weights of 1, 3, 9 and 27 kg. To check the weigh of a subject for that weight you will need to distribute the weights on the left and right pane to create the proper imbalance.
If your subject is on the left pane, there is a unique positions of the weights left/right/unused that lets you balance the weights with the subject.
Now if you count -1 for every weight on the left pane and +1 for every weight on the right pane, your total is the value that is assigned to the letter.

For example, take F. F = 6. To weigh 6 kilo you put your subject you want to weigh on the left pane, 9 kilo on the right pane and 3 on the left. This gives a value of 0. The maximum is M = 3 where you have 9, 3 and 1 on the right side.

So in some sense you are weighing the values of the words by weighing the letters literally with a balance.

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    $\begingroup$ Nicely done! Re your last spoiler: rot13(Gur nofgenpg bs gur ceboyrz lbh'er qrfpevovat jbhyq whfg or onynaprq greanel, juvpu vf jung jnf vagraqrq.) $\endgroup$ Dec 8, 2021 at 16:18
  • $\begingroup$ Dang, I had thought about using rot13(greanel), but couldn't figure out how to extract a negative component. Nice puzzle and solution! $\endgroup$
    – LOTGP
    Dec 8, 2021 at 16:23
  • $\begingroup$ @LOTGP Same! I even looked at rot13(fvtarq ovanel) for a while and then got too caught up in the periodic table idea! $\endgroup$
    – Crimsonfox
    Dec 8, 2021 at 19:05
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Partial Answer

Santa's rule for deciding who is naughty or nice depends on the the result of a mathematical or chemical equation. A positive or balanced result ends up with a nice child, otherwise a naughty child

Observations

- There are a number of terms relating to maths. Positive, negative, unbalanced, quarter (25?), realistic, few, some, chance, 42, unindebted (0?)

- No child appears to be naughty based on their first answer, their second answer (possibly combined with the first) seems to be enough to make a decision

- From the hint, each letter gets assigned a value based on being positive, negative or unbalanced (maybe +1, -1 and ??)

- If pos and neg are +1 and -1, all letters in CULTURAL would need to be positive to get 8

- "on"=-3 suggests it's not just +/-1. Do you apply all 3 (pos/neg/un) to each letter somehow? - Per the hint, yes.

- Initial thoughts were the numbers correspond to atomic numbers, then I dropped the idea, then with the latest hint, I'm considering it again

S: Ok kids, no naughty words please. Let's start with you, Alice. What do you want for christmas?

A: I'd like a real baby dragon!
S: Be realistic
A: Mom and Dad unindebted
S: What color do you want the dragon to be?

B: A quarter dollar.
S: That was close.
B: Maybe just a few sweets, please.
S: Forget it.
- Quarter dollar - 0.25, 25, 1/4, silver

C: A Beverly Hills mansion and world domination
S: Sure!

D: Cultural commercialisation
S: Ho ho ho! You have so much positivity!


E: The answer to life, the universe and everything
S: Don't be so negative.
E: Some candy?
S: Too late.
- Does the "too late" suggest that he made his decision after the first line
- First line - 42?

F: Is this a bad joke, Santa? My father told me everything about you
S: Perhaps. You still got a chance, though. What is it that you want?
F: A trip to queenwood and some arsenobenzene.
S: Ok, nevermind. You're an extremely unbalanced young boy.
- First line might be irrelevant as he only asks for something on the second

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    $\begingroup$ I's "That was close" or "You still got a chance" means the words so far are not eliminatory, or almost are for the first sentence. $\endgroup$
    – Florian F
    Dec 6, 2021 at 20:34
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    $\begingroup$ The only intentional clues are within what Santa says (although only a few of his sentences contain a clue). Any wrong word at any point will make a child naughty. $\endgroup$ Dec 6, 2021 at 20:58

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