0
$\begingroup$

A total of 10 friends came to my house for a party.

Halfway through the party, while we were having dinner, I noticed only 9 friends present in the dining room. A few minutes later, the missing friend came out from my study and joined our dinner.

After the party ended, I entered my study and saw a note:

Nice. Gotta crack that secret now

Unsure of its meaning, I put it away. As a music fan, I started my computer and typed "Never Gonna Give You Up" into the YouTube search bar, only to find a bunch of digits on the screen:

20247

I began to suspect that the naughty friend had sabotaged my computer. Curious, I proceeded to type the lyrics to Never Gonna Give You Up by Rick Astley, and here was the result:

36557
47571238
1285674
45436400

83784862
7144

20247
20842
2083124
20144
2004
20812144

3440822
83828255504
35777866
575713074

13421862
58125458

20247
20842
2083124
20144
2004
20812144

Increasingly confused, I started to wonder: what could possibly be the meaning of that note?


The lyrics for reference:

We’re no strangers to love
You know the rules and so do I
A full commitment’s what I’m thinking of
You wouldn’t get this from any other guy

I just wanna tell you how I’m feeling
Gotta make you understand

Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you

We’ve known each other for so long
Your heart’s been aching but you’re too shy to say it
Inside we both know what’s been going on
We know the game and we’re gonna play it

And if you ask me how I’m feeling
Don’t tell me you’re too blind to see

Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you

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1
  • 2
    $\begingroup$ I feel Rick Rolled... ;) $\endgroup$ Jul 17 at 4:30
4
$\begingroup$

The first and most obvious thing to notice is that

we appear to have one digit for each word in the lyrics, and when the same word recurs so does the same digit. So there is apparently a mapping from words to digits, which we need to find.

The next is that

the digits that appear are precisely 0..8; there are no 9s. This suggests that maybe we are reducing something modulo 9. For some reason, there are fewer of {0,1,6} than of {2,3,4,5,7,8}, but this is probably just coincidence.

It looks as if

case is not significant, because "a" and "A" both map to 1, and "You" and "you" to 4. Also, "no" and "on" both map to 6, suggesting that maybe we're just adding up per-letter values (or multiplying them or something, but adding seems simplest and most likely). The fact that a->1 seems promising, too. I guess that we will ignore the apostrophes.

Let's run with this idea and see whether it works.

We have you=4, your=8, youre=2 so if we're just adding things per letter then r=4, e=3. That makes the earlier observation that a=1 look less hopeful. We have we=5 and were=3, which is at least consistent with this. Let's keep trying to build up a mapping from letters to values and see what it looks like. If we=5 and e=3 then w=2... oh, that's suggestive. QWERTY keyboard column numbers? Yup, that seems to work.

So what's happening is that

each letter key is being translated into its position in its keyboard row (apparently apostrophes and spaces do nothing) and then each word is replaced by the sum of its letters' values, modulo 9.

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4
  • $\begingroup$ Well done! Now you can go a step further and figure out what the content of the note means :) $\endgroup$
    – L. F.
    Jul 17 at 15:13
  • $\begingroup$ rot13(Ol gur jnl, gur gra sevraqf ner fhccbfrq gb fvtavsl gur gra qvtvgf, jvgu gur zvffvat anhtugl sevraq orvat avar, juvpu vf abg bayl zvffvat va gur bhgchg ohg nyfb na rffragvny cneg bs gur genafyngvat nytbevguz) $\endgroup$
    – L. F.
    Jul 17 at 15:17
  • $\begingroup$ It seems to me that rot13(gurer'f n zber boivbhf qvtvg sbe n sevraq fcrpvsvpnyyl qrfpevorq nf "anhtugl" gb ercerfrag)... As for the note, it seems to say rot13(r) but it's not obvious to me what actual significance that has. $\endgroup$
    – Gareth McCaughan
    Jul 17 at 23:21
  • $\begingroup$ rot13(Gur "boivbhf" rkcynangvba bs "anhtugl" vf boivbhf abj gung lbh zragvba vg! Fbzrubj vg rfpncrq zl zvaq juvyr V jnf pensgvat gur chmmyr.) Indeed - the note refers to the number, which is simply an Easter egg for the puzzle with no real significance. By the way, I am really impressed by the way you looked for clues and put them together to solve the algorithm. $\endgroup$
    – L. F.
    Jul 18 at 1:43

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