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Trapped in a Room
I suspect it's something like reddit.com/r/riddles/comments/4ylgi0/comment/d6omol6
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Numerical sequence puzzle: 38, 104, ?, 1358
Not particularly elegant (ax^2 + bx + c where a = 1188/7, b = -726/7, c = 38), but certainly simple, yes.
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Caress me gently
Jryy, gurer hfrq gb or avar cynargf
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Can the distance of any 2 points inside an isosceles triangle be more than the length of the equal sides?
For any two interior points (A and B), draw a line through them that intersects the triangle at C and D. Let E be a vertex such that CDE >= 90 degrees. Now AB <= CD, and CD <= CE (the hypotenuse of CDE), and CE <= x (because C, like the rest of the triangle, fits within a circle of radius x centered at E). So AB <= x.
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Making a multiplying magic square
A direct answer would pretty much give it away. Here's a hopefully less obvious hint: How would you construct a 3x3 multiplying magic square where the nine numbers could be any nine distinct positive integers?
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Explain answer to "Adventure beginning by way of hill. One in 10!"
A web search confirms that it is. merriam-webster.com/dictionary/tor
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Fewest number of prisoners needed
That's a minimum, but is it achievable? It's not obvious how to construct a list of assignments that maximizes efficiency.
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What Language Is This?
By inference. "First three lines have some carets then :: then an equal number of carets; looks like code for 1 = 1, 2 = 2, 3 = 3. Next two lines look like code for 1 + 1 = 2, 4 + 3 = 7." And so on.
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What Language Is This?
added 283 characters in body
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Why, crystal ball? Why?
rot13(guerr gb gur cbjre vf gjbbarrvtugfrira), but I don't know how (gjbbarrvtugfrira gb gur cbjre bs bar) is meant to be ruled out.
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Yes, but... where am I?
Is it a zntvp rlr chmmyr?
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Tatiana thinks of two numbers
If the order of the numbers is unimportant, then there are 1000 ways to choose the same number twice, plus C(1000,2) = 499500 ways to choose two different numbers, so 500500 total. If the order is important, then yes, there are 1000000 ways.