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There's a cool new cybercafé in town called #DECAFE

The café charges a fee to use their computers, but if you BYOC (bring your own computer) you can get on their internet free with any purchase... if you know how!

After you pay, the cashier says a sentence. If you reply with the correct number, they will hand you a slip with credentials.

You eavesdrop as the four people in front of you acquire internet credentials:

Cashier: Aloof whale swim forth.
Customer #1: One

Cashier: Tasty warm pasties contain stuff.
Customer #2: Two

Cashier: Pinkish fish adds distinct flavour on your bagel: robust smack.
Customer #3: Three

At this point, you figure it's easy enough, but then you're thrown for a loop when the next number is not four.

Cashier: Toxic frogs dispatch.
Customer #4: Sixty

After you've made your purchase, the cashier says:

Our cat can lick ice, you know.

What number must you say to obtain internet credentials?

Clarification

The challenge-response format is just intended to be a fun wrapper (and to make solving the puzzle easier by providing explicit known hidden messages): the challenges conceal the appropriate responses plainly using steganographic methods.

Hints

#DECAFE is a color as pointed out in the comments, but that's not what counts.

Every word is important, but only a handful of letters are meaningful.

The spelling of a number (in English) is relevant in at least one challenge. Not all numbers are represented the same way.

The cat could also pour ale without changing your answer. Similarly, the pasties could also contain pilaf, but not meats. Moreover, the whale could instead be a goose or a drake or possibly a manatee, but not an otter or a squid.

This phrasing with cryptical prose forms hint

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    $\begingroup$ I'm guessing #DECAFE is a colour. $\endgroup$
    – user88
    Jun 26, 2016 at 19:53
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    $\begingroup$ @Will Any more hints? $\endgroup$
    – pajonk
    Jun 29, 2016 at 6:52
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    $\begingroup$ @Arth Assume if anything is needed it's part of the café's decor. :) $\endgroup$
    – Will
    Jul 6, 2016 at 16:02
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    $\begingroup$ @David Nope, the responses could be any form for a number that would be more or less understood by most English speakers. That is to say SIXTY and 60 are both possible as is at least one other representation. 60 would not be 6D though that might be a fair representation for 109, however I will say none of the challenges in the question use hex in that manner. 6T is right out. $\endgroup$
    – Will
    Jul 24, 2016 at 10:42
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    $\begingroup$ I'll also add that 60 would be unlikely (not impossible, but I intentionally avoided something that could be used to make it possible to keep the puzzle more straightforward) for a reason that will be quite obvious once this is solved. $\endgroup$
    – Will
    Jul 24, 2016 at 10:56

4 Answers 4

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The number you should say is:

Thirty-four point four.

We can decode each phrase by ..

... taking words in pairs. Each word pair represents a letter (or character) and the lengths of these pairs taken as hex number yield the ASCII code of that letter. In other words, the ASCII code is:

c = 16 · length(w1) + length(w2)

There's a special rule, though. The name of the café hints at ...

... the importance of the letters in DECAFE. These letters are all valid hex digits. These letters are special when they come at the end of a word:

A single word whose last letter is a valid hex digit also represents one letter. The corresponding ASCII code is the hex number made up of the length of the word without the last letter plus the hex digit at the end:

c = 16 · (length(w) − 1) + hex(last(w))

With this method, the first phrase becomes:

Aloo·f whal·e swim forth. → 4f 4e 45: ONE

Second phrase:

Tasty warm pasties contain stuf·f. → 54 77 4f: TwO

Third phrase:

Pinkish fish adds distinct flavour on your bagel: robust smack. → 74 48 72 45 65: tHrEe

Fourth phrase:

Toxi·c frogs dispatch. → 4c 58: LX, which is sixty in Roman numbers.

The last hint:

This phrasing with cryptical pros·e forms hint → 48 49 4e 54: HINT (Ha!)

So, now to my passphrase:

Our cat can lick ic·e, you know. → 33 34 2e 34: 34.4

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  • $\begingroup$ You're painfully close on some of your points... $\endgroup$
    – Will
    Sep 16, 2016 at 20:05
  • $\begingroup$ Interestingly, though you have cracked parts of it (kudos on those!), you've gotten as far as you have through a series of coincidences related to the underlying rules in play. Of course, the cat challenge is intended to ensure more complete understanding. ;) Also, I will say you've got the last hint wrong. $\endgroup$
    – Will
    Sep 16, 2016 at 20:17
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    $\begingroup$ Okay, I'm tried. That HINT is pretty self-referential now. :) $\endgroup$
    – M Oehm
    Sep 16, 2016 at 20:44
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    $\begingroup$ You've got it! I'll wait to accept so more people might look and upvote. :) $\endgroup$
    – Will
    Sep 17, 2016 at 16:31
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    $\begingroup$ @Simon There's an ASCII table on the wall - it is a cybercafé after all (possibly uninteresting and overly vague aside: my motivation for saying this is a reasonable assumption beyond the fact it's a cybercafé is a small local chemistry-themed food franchise with chem equations and a faux periodic table on the walls). It also would not be unreasonable for one to print a copy of a table on a card/insert that fits in their wallet, which they'd probably have out already anyway. $\endgroup$
    – Will
    Sep 19, 2016 at 10:02
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So, this is something of a horrible stretch, but I figured I'd share where it got me.

While the '#' at the start of "#DECAFE" certainly appeals to a hex interpretation, the hints seems to suggest that 'count'-ing letters may be key. Towards that end, if we look at "DECAFE" as a sequence of numbers we get 4-5-3-1-6-5. Using these in a rolling fashion over each word (with in-word wrapping -- eg the 5th letter of "hope" is 'h'), we get oeif for the first interaction (this is where it gets stretchy) which is close, both lexical-ly and phonetically, to oeuf meaning zero (which isn't even one... so not sure where to take that).

Continuing with the decoding (using the offset from the first interaction) we get T-W-T-A-U, or T-W-Tau, which I'm not clear on equating to "TWO", but wanted to share. It seems to break down into gibberish at the third -- "p i a t o y b s c" (maybe "Pi at 0 -ybsc"? No real clue), but I'm hoping this sparks something for others, or as I fear is more likely, at least prunes possibilities that others need try.

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  • $\begingroup$ Tau is 2pi - probably not much help $\endgroup$
    – Jasen
    Aug 6, 2016 at 3:48
  • $\begingroup$ Unless Tau = 2*pi is meant to reference a full circumference which gives T-W-circle which would certainly be close enough to "T-W-O" for me. However, I do feel that this remains something of a stretch. $\endgroup$
    – SingularityNow
    Aug 7, 2016 at 7:32
  • $\begingroup$ Actually, the most recent hint makes all of this a moot point. $\endgroup$
    – SingularityNow
    Aug 7, 2016 at 7:35
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This almost fits except for a couple of issues:

Only the letters e and x are significant. Count back from the end of any word that contains an e, its position from the end is the score. Include punctuation in the count.

Whale ends in e and scores 1, pasties have second to last letter e and score 2.

x counts for 20 per letter counted back rather than 1.

This fits with most of the hints except that

1. there's only one x example so it's really a leap with that one.
2. The comments suggest that spelling is important and that not all numbers are represented the same way.

These rules would lead to an answer of

2 for the final question - the comma counting as the starting point

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  • $\begingroup$ Quite innovative. $\endgroup$
    – SchrodingersCat
    Aug 7, 2016 at 10:20
  • $\begingroup$ How does this work if "bagel" would only score 2? $\endgroup$
    – CasperTheFriendlyCode
    Aug 31, 2016 at 18:42
  • $\begingroup$ @Casper They're counting the colon, though that's obviously a stretch. I've considered amending the fourth hint to explicitly nullify this "solution," (the bagel could just as easily be a torus and sentence #4 need not have an "x") but that would possibly be a bit dodgy of me. $\endgroup$
    – Will
    Aug 31, 2016 at 19:03
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I'm not sure how this rule can be transmuted to the first three examples, but I did notice that if "Toxic frogs dispatch" is spelled backwards, I believe "sixt(y)" is the largest number that can be spelled out with at most one letter missing from the end. I can't work out any number larger than one that can be spelled backwards in "Our cat can lick ice, you know.".

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  • $\begingroup$ I can see "nin(e)" $\endgroup$
    – Jasen
    Jul 2, 2016 at 5:26
  • $\begingroup$ Tasty... has "fo(u)r" so maybe last letter missing. $\endgroup$
    – Jasen
    Jul 2, 2016 at 5:29
  • $\begingroup$ but Pinkish... has "si(x)", maybe the longest number is required. $\endgroup$
    – Jasen
    Jul 2, 2016 at 5:31
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    $\begingroup$ Pinkish... doesn't have three $\endgroup$
    – Jasen
    Jul 2, 2016 at 6:55
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    $\begingroup$ As fascinating as this debate is it's not going to get you anywhere (well, perhaps part of it could), plus FWIW I see CMLVIII. $\endgroup$
    – Will
    Jul 8, 2016 at 20:24

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