Can you solve the secret sauce riddle?

Originally published at: https://boingboing.net/2019/09/16/can-you-solve-the-secret-sauce.html

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secret sauce

If it’s that much of a secret, don’t eat it. So say I.

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All of these riddles can be solved with a $5 wrench, just sayin’…

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The safe deposit box is a lie. The chef has swallowed the recipe to keep it out of enemy hands. And it’s not going well for him—look how distended his tummy is.

image

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Would a Buck Three Eighty wrench work? Asking for a friend on a budget…

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This isn’t very clear to me, even after seeing the answer. The reasoning here seems fuzzy.

Why do you assume the interrogator has it narrowed down to only two possibilities before the last question? Can’t it have any number of possibilities so long as the last question eliminates all but one option?

Why is it safe to assume that the answer must be a perfect cube? If it’s just to narrow the search space, why is that allowed? If we assume the answer to the third question is a truthful “no” then the interrogator still gets an answer but we are boned.

For instance, consider this scenario:

If the interrogator thinks the number is between 13 and 499, we know that was wrong, so the real number is between 500 and 1300.

Further, if the interrogator thinks the number is a perfect square, we know that is wrong, so the number must not be a perfect square.

Further, if the interrogator thinks the number is not a perfect cube, we know that is right, so the number must not be a perfect cube.

Therefore, the interrogator has limited his choices to numbers between 13 - 499 that are perfect squares but not perfect cubes: 16, 25, 36, 49, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. We know the interrogator was able to narrow this down to a single number after the last question. It’s not 100% clear what is meant by “second digit” in this case, but depending on that definition, the interrogator must think the number is either 16 or 81, he has a single number, good for him, even though we know it is wrong.

But we know the real number is between 500 - 1300, is not a perfect square, and is not a perfect cube. Our pool of numbers is still too high to get an answer. What am I missing?

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It’s Thousand Island Dressing. It’s always Thousand Island Dressing.

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In your scenario, the interrogator wouldn’t have been immediately sure about the number after finding out if the second digit was 1, because he would have crossed out 81, since it’s both a cube and a square.

So not 81…so your alternate scenario wouldn’t have worked, and the given solution is the only scenario that does.

(I don’t think many people would ever call the 1 in 16, the second digit.)

The wording here is strange indeed. I guess I should spoiler:

Ultimately, there are only two numbers that are both perfect squares and perfect cubes that are between 13 and 1300, namely 64 and 729. The only perfect square with a second digit of 1 is 81; the only perfect cubes with a second digit of 1 are 216 and 512.

So, presumably, the interrogator believes the number is a perfect cube, but not a perfect square, but we know that the number is a perfect cube and a perfect square. And presumably the interrogator believes the number to be smaller than 500, or he wouldn’t have asked about the perfect square. Ergo, the number is… 729?

ETA: That is, of course, wrong.

I think so, too. I ended up with 4 ways that the interrogator could think he’s got the answer, and in two of those ways, you could know what he did wrong and get the ‘real’ answer. Two other paths lead to too many possibilities. Therefore, you can’t be sure of the real answer imho.

Not putting SPOILERS because video thinks I have the wrong answer.

According to my calculations, if the chef’s answers to the 3 questions are:
FFT --> 512 with YES on final question, 1000 with NO
FTF -->1156 with YES
TFT–>216 with YES
TTF–>81 with YES

Substituting the chef’s fake answers for questions 1 and 2, we get the truth, which implies

TTT–>64
TFF–>Too many to know for sure
FTT–>729
FFF–> Too many answers

You don’t need to narrow down to 2 possibilities, in fact only FFT gets us to that state. FTF leads to 11 possibilities which could collapse to 1; TFT leads to 4 possibilities which can collapse to 1; and TTF leads to 18 or so that could collapse to 1.

So I think the video is wrong. There are 5 numbers the thieves could land on: 512, 1000, 1156, 216, or 81. And trying to find the true answer will lead you to either 64, 729, or a whole lot of other possibilities.

Prove me wrong!

EDIT: Ok, It looks like they have an “out” and their result is correct

The interrogator says, before the final question, “Just one more question and we’ll be done here” so that is in effect saying, I’m guaranteed to know the truth once I hear this answer, i.e., there can only be two numbers left at that point.

Proved myself wrong.

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I appended this to my TL;DR post above, but the interrogator says

If you just tell me whether the second digit is a 1 we’ll be done here.

So he knows that his question will give him the final answer, meaning he was down to two possibilities at that time.

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Yep. Unfortunately, that extra bit of info was not captured in the summary slide. The summary just says the interrogator thinks they have the number after they get the answer, not that they were guaranteed to have the number with just one more question.

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If the interrogator believes the number is over 500,

  1. FFT --> 512 with YES on final question, 1000 with NO
    “1000 with NO” is actually answered by more options than 1000, so that’s not a possible scenario.

  2. FTF -->1156 with YES
    The interrogator could have thought this one. But it does lead to no knowable answer as a non-solution.

  3. TFT–>729 with YES
    (Wasn’t meant to be 729)

  4. TTF–>81 with YES
    If the interrogator believes the number’s under 500…
    …then the interrogator can’t believe that the number is 81 and believe the number is also not a cube or not a square.

512 and 1000 are the only ones that fit, what are the others?

That should say 216. Fixing it

TTF–> 81 < 500, is a square, and is not a cube.

Yeah; I followed a similar reasoning for whether the second last digit is a one. I figured the chef must have answered that it is a 1, as this leads to a definitive answer, but if he had answered no, then the interrogator would have asked more questions.

My overall reasoning is as follows (these are the chef’s answers to the interrogator):

if >500:
  if square and cube, answer must be 729, so don't need the last question, so he didn't answer this
  if square and not cube, answer is 1156
  if cube and not square, answer is 512
if >500:
  if square and cube, answer must be 64, so don't need the last question, so he didn't answer this
  if square and not cube, answer is 81
  if cube and not square, answer is 216

Now, we know that the chef lied about the square, and told the truth about the cube. But as shown above, he answered different things to both of them. That means in reality, the answers must be the same. So either the number is both a perfect square and perfect cube, or is neither square nor cube. The latter case makes it impossible to solve the puzzle so can be discounted (yes, that’s kind of cheating, but I don’t care). So that means the answer is both a square and a cube. Which means it’s 64 or 729. But not knowing whether it’s above or below 500, I can’t get a definite answer. Fuck it, I’ll just check both boxes.

Went over it again, you were right.

The interrogator says, before the final question, “Just one more question and we’ll be done here” so that is in effect saying, I’m guaranteed to know the truth once I hear this answer, i.e., there can only be two numbers left at that point.

You’re right about that making the difference to the inconclusive parts.

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Looking at the youtube comments, they’ve added a clarification:

Riddlers, we have one more thing to add to the rules! Read this while you pause: the last thing the interrogator says to the chef is: "If you just tell me whether or not the number’s second digit is one, we’ll be done here.” You don’t know whether the chef answers that truthfully, but whatever he says, that makes the interrogator think he knows where the recipe is.
Thanks everyone, now back to riddling!

Yeah…I guess there’s some value to RTFA.

Or in this case WTFV