77

No questions are required!


64

These should do it: Just to show another example:


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55

Answer: Reasoning:


50

@Jay already found the solution to this, but I wanted to expand a little more on why it's the only solution:


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40

Note though that this only works because this particular maze has no straight moves available (i.e. intersections where you can't turn but only go forward). For example, using the same rules, if you remove the vertical line directly below the 2x1 block...


37

I think this could be an answer:


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33

A shortcut to get the correct answer, assuming that one exists, is to simply assume that A, B and C are all knights, and thus speak the truth. In this case, C will obviously answer "Yes." And since the question implicitly assumes that C's answer is the same for any possible scenario, C must always answer "Yes." This, by the way, is a very handy exam-...


33

Alice's house number is Reasoning


32

Here is an answer that I think is slightly easier to understand:


28

OK, let's actually take this seriously. As others have said, this is the so-called St Petersburg paradox, and the reason it isn't really much of a paradox is that (1) an extra dollar matters much less when you already have a lot of money and (2) our counterparty may not actually pay up. So let's model that. The simplest somewhat-plausible way to handle #1 ...


28

Here is a simple strategy of how they could do it Proof


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Answer Reasoning Furthermore


26

It can be done in Solution


26

Part 1 The final solution (finally)


24

I think the French will say The English says "M", the French says "M", the German says "M" German "D", French "V", English "S"


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23

4-button method


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23

The person telling the truth is: because: and consequently, the killer is:


22

I've been really enjoying these puzzles. This was the best one yet. Reasoning:


21

Here is the solution Reasoning


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Initial bounds So at least one of $A,B,C$ must be Narrowing possibilities So the only option Final answer So the final answer is


20

The property is that


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Hint 1 Hint 2 Hint 3 Answer


20

The answer is: Here's the way you get that number:


20

If a rectangular piece of chessboard is $a\times b$ squares in size, then its diagonal squared is $a^2+b^2$ and its area squared is $a^2\cdot b^2$, and therefore the quantities $a^2,b^2$ are the roots of the quadratic equation $x^2-D^2x+A^2=0$ where $D,A$ are the diagonal and area. But this is enough to determine $\{a^2,b^2\}$ completely: these values are $\...


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