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I'm obviously dating up, because I can't figure out what my girlfriend wants me to buy her for Christmas. When I asked her what she wanted, she gave me the three puzzles below. The only hint she gave me is that she only wants one item.

A few things that might help:
She's really lucky. (I mean she is dating me.)
She likes card and board games. (Setters of Catan is her favorite. No, it's not that. She already has it. And 5 expansions, but that's probably not helpful)
She likes animals (especially dogs and cats) and had a cat named Ralph and a dog named Bingo
Her favorite song is that double rainbow song.

Puzzle 1:
C A R E       2 1 0 0
R A C E       2 2 0 0
T A R E       2 2 0 0
T O R E       2 1 0 0

Puzzle 2:
2 1's & 1 16 + slang human head

Puzzle 3: (There has to be a couple of steps for this one, right?)
H zl dnm fghms zcdl en zlmx.
'Hl dqux zklmx ast h ddeoqq dml.

Fffioswx ffmpqq defjpstw fn j bbmtxz hpsx po finu.
Gj j cdffnp dfmmppstt ejnptx dfnpt.

Hint 1:

I've figured out the overall answer is definitely a card game.

Hint 2:

Puzzle 2 has a chemical element to it.

(Meta Note)

The three sub puzzles are obviously needed to solve the puzzle as a whole. The other 'hints' may or may not be helpful after the sub puzzles are solved. On the other hand, the hints (or parts of them) could just be there to distract from the real solution.

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    $\begingroup$ (1) If you can’t figure out what your girlfriend wants, no conclusions can be drawn from this.  You could be dating up, down, or sideways.  (2) If she’s dating down with somebody who doesn’t understand her, how is she lucky?  Is the bit about luck an actual clue, or just egotism? (3) I don’t know what “that double rainbow song” is. Seriously.  If this is an actual hint, can you please be more explicit?  If we need to guess what song you’re talking about, the question should probably be tagged [knowledge] or [trivia]. $\endgroup$
    – Peregrine Rook
    Commented Dec 24, 2016 at 19:36
  • $\begingroup$ @Peregrine Rook I've retagged the question. $\endgroup$
    – Kevin Rock
    Commented Dec 24, 2016 at 20:52
  • $\begingroup$ OK, it's been three weeks.  Are you going to give a hint? $\endgroup$
    – Peregrine Rook
    Commented Jan 15, 2017 at 3:57
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    $\begingroup$ It's a ring. She wants a ring. I didn't even bother reading your puzzle; the answer is obvious. $\endgroup$
    – Ian MacDonald
    Commented Jan 17, 2017 at 20:02
  • $\begingroup$ @IanMacDonald hahaha :P $\endgroup$
    – Mr Pie
    Commented Jul 18, 2019 at 15:17

4 Answers 4

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If I can resurrect this one, I think I've spotted the links between all the previous partial solutions, worked out an element that had been missed by all, and can explain the additional hints in the text. Your girlfriend wants you to buy her:

Exploding Kittens, the card game

Puzzle 1 (solved by @PeregrineRook):

Is a Mastermind puzzle, which produces the answer TACO.

Puzzle 2 (solved by @ThirupathiThangavel):

Is a simple word puzzle, which produces the answer WATERMELON.

Puzzle 3 (worked on by @Techidiot with a comment that came very close from @GarethMcCaughan):

Part 1 actually translates via rot-1 as 'I am one thing made of many. I'm very manly but I prefer men.'
Part 2 translates via rot-25 as 'Whenever people discover me I always grow on them. If I become colorless, wisdom comes.'
These clues lead to the answer BEARD:
I am one thing made of many. - One beard is made of many hairs.
I'm very manly but I prefer men. - A beard is considered a manly thing to have; it 'prefers' men in the sense that it's usually men it grows on.
Whenever people discover me I always grow on them. - A beard quite literally grows on a person...
If I become colorless, wisdom comes. - Grey hair (or a grey beard) is a sign of age and 'wisdom comes with age'.

However, there was an extra clue hidden in the bold and italicised letters of Puzzle 3 which nobody spotted (because nobody was looking for it):

The letters produced by the rot operations on the bold letters give: AHYIRUPSD, which anagrams to 'HAIRY SPUD'. Since 'spud' is another word for 'potato' this leads to the answer HAIRY POTATO (don't see it yet? Bear with me!).
Meanwhile, the letters produced by the rot operations on the italicised letters give: EDNREREGRHI, which anagrams to 'RED HERRING' and has no further utility for the puzzle!

Why do these lead to the answer above? Because:

4 of the 5 types of 'cat card' in the original game are called TACOCAT (pleasingly palindromic), CATERMELON, BEARDCAT and HAIRY POTATO CAT.

There were other clues in the preamble too:

1. She's really lucky - Exploding Kittens game is partly a game of chance, in the way the deck is shuffled and hands are dealt.
2. She likes card and board games - It's a card game.
3. She likes animals (especially dogs and cats) - It's all about cats!
4. She had a cat named Ralph - The fifth 'cat card' in the game is called the RAINBOW RALPHING CAT.
5. Her favorite song is that double rainbow song - Again, as per 4.

The other answers between them each had one component of the final solution. Hopefully this finally now brings them all together in totality with the fourth previously unspotted one, and you can get down to the shops PRONTO! Here's hoping your girlfriend is a VERY patient woman ;-)

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    $\begingroup$ Or build a time machine and travel 2.5 years back... :) $\endgroup$
    – sunfishho
    Commented Jul 18, 2019 at 16:24
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    $\begingroup$ Way to go after all this time :) $\endgroup$
    – Rubio ♦
    Commented Jul 18, 2019 at 23:22
  • $\begingroup$ Congrats @Stiv. I wondered if anyone would get this. Here's a green checkmark for your prize! $\endgroup$
    – Kevin Rock
    Commented Jul 24, 2019 at 19:03
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    $\begingroup$ @KevinRock As soon as I saw TACO and WATERMELON there was only one thing on my mind! :) $\endgroup$
    – Stiv
    Commented Jul 24, 2019 at 22:27
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Puzzle 1 looks like

Mastermind, a guessing game a little like hangman except you guess the entire sequence1 all at once.  Your adversary (i.e., the controller of the game) responds with how many symbols you have right, and how many of them are in the right position.  Some implementations always give you $n$ responses, even though the last $n-2$ are undefined and are always given as zeroes.  So,
$\begin{align}\texttt{CARE}&&2100\end{align}$
tells us that (exactly) two of the letters C, A, R and E are correct (in the word to be solved), and one of them is in the right position.  Not much to go on.
$\begin{align}\texttt{RACE}&&2200\end{align}$
tells us that two of the letters R, A, C and E are correct — but we already knew that, since these are the same letters we had before.  The new information is that both of the correct letters are now in the right positions.  This means that one of the letters that was in the wrong position in CARE is now in the right position.  From that we can conclude that either A or E is in the right position (and the other is not in the word at all), and likewise for R and C (as positioned in RACE).
$\begin{align}\texttt{TARE}&&2200\end{align}$
No change in the information about A and E.  This tells us that either T or R is in the right position (as positioned in TARE), and the other is not in the word at all.  But we already know that R does not belong in the third position, so it must not be in the word at all, and T must be the first letter.  This narrows it down to TAC_ (where the _ is not E or R) or T_CE (where the _ is not A or R).
$\begin{align}\texttt{TORE}&&2100\end{align}$
tells us that we still have two correct letters, but now only one of them is in the right position.  Well, we know that T is the first letter.  If E is in the word at all, it is in the last position, so it must not be in the word at all, and we must have TAC_.  But we do have two correct letters, so the O must be in the word, but just not in the second position.

So, in conclusion, $\large ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textrm{TL;DR}$

The word is $\texttt{TACO}$.

________________
Footnote 1: Mastermind is not necessarily played with words.  It can be any sequence of symbols, including colors.

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Puzzle 3 Part 1

Rot 1 gives -I am eon ghint adem fo amny. 'Im ervy almny btu i eefprr enm.-> I am one night made of many. I'm very manly but I prefer men.

Puzzle 3 Part 2

Rot 25 gives - Eeehnrvw eelopp cdeiorsv em i aalswy gorw on ehmt. Fi i bceemo celloorss dimosw cemos -> Whenever people discover me I always grow on them. If I become colorless, wisdom comes.

And

The bold letters from the final lines are - aiyIetlsw
The italic letters from the final lines are - oalehvpgohi

Next step will be

To apply rot/rearrange the letters to find something meaningful. ATM, there are various things coming out of these letters.

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  • $\begingroup$ 3:2 sounds like it might possibly be hair. (White hair is "really" colourless; thin fibres of glass with a matt surface would have a similar appearance. Having white hair is a sign of age. Almost everyone has hair, though "always" seems like an overstatement if this is right.) $\endgroup$
    – Gareth McCaughan ♦
    Commented Dec 24, 2016 at 23:21
  • $\begingroup$ @Gareth- I'm not sure if it's riddle. May be we need to get the bold & italic letters from these lines and perform operations. Will look into this tommorow(in case if it remains unsolved) $\endgroup$
    – Techidiot
    Commented Dec 25, 2016 at 5:58
  • $\begingroup$ Combining my answer to Puzzle 1, the clear text of Puzzle 2, and Gareth McCaughan’s response to the interim solution to Puzzle 3 Part 2, we seem to be heading in the direction of this (hover).   ROT13 version: ungf -- fcrpvsvpnyyl, Jvagre Onfu ungf. $\endgroup$
    – Peregrine Rook
    Commented Dec 28, 2016 at 22:27
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Puzzle 2:

2 1's & 1 16 + slang human head

H2O + slang for human head
Watermelon

(Thanks to Will)

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    $\begingroup$ Ummm... melon? ;) $\endgroup$
    – Will
    Commented Jan 17, 2017 at 20:34

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