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34

Building on samm82's answer, and fixing the French fashion designer answer as Enigma said, you get As Graylocke observed, Removing every other letter reveals i.e. the solution is Edit: just realised:


34

Alice Bob


29

I think the answer may be because


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This answer was a group effort between @Graylocke, @berkeleybross, and myself, with a little confirmation from @Enigma, so I'm more than happy to make this a community wiki answer (unless there are any objections or @Stiv wants the +2 rep for accepting XD). The answers to the questions: What you should have done is


22

Edit 2: The game they're playing is The rules are Let's analyze the first game. Alice starts with "Jingle bells." Bob goes for "I saw Mommy kissing Santa Claus." Alice responds with "Rudolph the red-nosed reindeer." Bob's turn next and he says "I can’t let you win next turn, so... Feliz Navidad." Alice responds ...


20

It's undefined although a slight tightening up of the question would make it defined. What the question lacks is a specification of what happens when a player reaches the limit of the universe. To be more specific: Suppose each player executes their optimum strategy of moving at maximum speed in the negative direction. What exactly happens at $t=1/3$ when ...


16

The capitals Rodney visits are ... How? What's with the "aeroplane stairs"? And the cities? In detail:


15

The puzzle seems to be referencing


15

Fundamentally, the issue is that For every fixed cop strategy, there exists a thief strategy that beats it. For every fixed thief strategy, there exists a cop strategy that beats it. For an easier picture, this is effectively what the game looks like: Cop chooses a real number $C\in(0,1)$ (basically $\liminf_{t\in\mathbb{R}^+} C(t)$ of their position) ...


13

I don't know if this is the right answer, but it seems... plausible? So... What does this mean?


13

Partial answer - figured out how to 'read' the pieces


12

The sergeant was told Answers to the questions: A list of the answers: There is a clue in the questions here So, sorting the words: So the message is:


12

Don't worry, there's nothing sinister going on here. Your wife is just happy because... Each of the lines of fruit emojis in the main graphic represents: If we use the 'key' provided in the additional information, we can make the following correspondences: This makes sense of the many references to your wife's 'good mood' and 'sounding out' the emojis (...


12

Expanding on Gareth's answer:


11

Perhaps the equation refers to the In particular, If that is the case, the equation is indeed true: Here $m$ has to be "Well, if you avoid the repetition at the end, you'll find something that's hard to tell if it's true or false. But it's also the key."


11

I think the year is The first gentleman is born on The second gentleman was born in Additionally,


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is right, basically because The problem with one of the two suggested approaches is that The space in which they're moving is sort of like a 1-dimensional hyperbolic space: they can get infinitesimally close to the boundary but they can never actually reach it. TL;DR: it seems that, on an open line segment, Zeno's paradox is actually true.


11

Cleaned up answer: To make things concrete, let's say that the cop's strategy is represented as a function c(t), which is dependent on the thief's trajectory w(t), and vice-versa. The cop's strategy is c(t) = max(2/3-t, w(t)). The thief's strategy is w(t) = c(t)/2. Now we can observe for the cop's strategy that We can also observe for the thief's strategy ...


10

I think the combination is Under net, counter and employ longest leg (10) Sports captains often realize even beginners get points (5) Oddly swindled by façade (4) Number of bakers sleep before noon? (5) Mess up plants without energy of Motown singer (7) Fantastic comic publisher associated with British universities (9) Poor chance: I am large and ...


10

Solved! The answers to the quiz questions are as follows: But - hang on a moment - there's something very familiar about the new barman, 'Tex'... What did he say to the Sergeant? "I'm four steps ahead of you"... There's something very susp- Wait! I know who he is! How can we go about spotting this pattern? Well, first note that quizmaster 'Tex' ...


10

You need Not a state secret, but still confidential. Becomes chaotic when unplanned. Found in New York, but not anymore. He's been lost without a trace. This is a site for those who create, solve and study puzzles. Nothing goes unnoticed here. Best to wear this in a fight.


10

Answer: Solving: Full list:


10

TL;DR First, and easiest, we can do it in: Using the principle of the: The method is as follows: You then just need to rearrange your pieces. Why does this work? Now that we understand that method, how can we do it better? We now need to prove that we cannot do better. However, this is impossible. The following is a sketch of a proof:


9

This playlist serves as inspiration to your friend when she attempts to solve: Why? Firstly, note that: Finally: PS Note a small hint concealed in the text:


9

The most obvious place to start is with I don't know anything much about these, but So: How, you ask, did I disambiguate in the two places where I did? Well, And of course


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It spells:


9

Astrid is trying to find: And its "formula" is simply: There could be many reasons why this isn't working for Astrid, which are well beyond the scope of this answer! Some explanation:


8

Okay, there's a lot at play in this puzzle, so I feel a partial answer is justified to get things going and see if anyone can build off the things I have found... First, let's address the 'PS' to the letter, which features this sequence of letters: RNEZR GFTGA BUULJ DXCCI VQPHQ SWKMY. What are these? To understand that, we need to consider them together ...


8

New answer: 1 question. Explanation: Outdated answer, for posterity 2 questions. First question: Now we will figure out who to ask the next question to: Now ask this group: Explanation:


8

This is a really nice puzzle! To break into it... So we know where the plane was leaving from - where was it travelling to? Without any coordinates to find this out (all the numbers are obscured by the coffee spill), we need to: The logic that I followed to solve this was roughly as follows: Finally, we can identify the 3 characters in the destination ...


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