bonanova
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Everything posted by bonanova
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Hi,
I haven't been around for a while. Had a personal incident last August or thereabouts that changed a few things, and I guess I quit thinking about puzzles for a while.
The site has a nice [new] look and feel. And a lot of new members. I don't see Martini anywhere - have we lost him?
Let me know if there's anything I can do.
- bn
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Hadn't thought of that one ... Nice!
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Nice. Especially mmiguel1's solution. I was unaware of the lb notation; otherwise each log base 2 would cost a "2". The Odd function smacks of floor ceiling and round functions and in spirit should be disallowed. But in letter, it's fine. ++ obeys the OP which should have stressed mathematical [not programming] functions, but did not. Follow on: Can it be done without [+, -, x, /] using a single instance of two functions?
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Related to the idea of the Berry paradox 1, 2, consider this definition from Onelook. Quick definitions (indescribable) ▸ adjective: defying expression or description ("Indescribable beauty") Suppose you are asked to debate the proposition: "The word 'indescribable', being an adjective, necessarily describes something. It is thus self-contradictory, lacking clear meaning, and should be removed from the language." Would you choose the Affirmative or Negative position; and what would your argument be? Have fun.
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Make 2 and 2 equal 5. That is, create an expression whose result is 5, using common functions and field operators, but only two constants, both of them 2. Anything from simple addition to inverse hyperbolic arc-tangent is permissible. Except: we do not allow round, floor or ceiling functions. Also no variables. So 2 - 2 + (x+x+x+x+x)/x is not allowed. You may use 2 only twice. So (2/2) + 2 + 2 is illegal. Square root is OK. Squaring is OK, but it costs you a 2. No other powers can be used. Enjoy.
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Edit: The OP suggests that it's only the worst case we want to optimize, not the average; but it falls a little short of being explicit on that point ... my bad. - bn
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Yeah, what Tuckleton said.
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Partial, but not the complete, answer so far. It's not a hard problem. I mused for a day or two without using paper before posting it. Full disclosure, I needed paper.
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Thanks for the WB It's OK to assume you find the switches all down. But, you know nothing initially about their connections. So you won't get the answer by assuming favorable outcomes to your first flip. You want to minimize the required number of flips [that implies worst-case analysis] with respect to n. Is there a preferred value [singular] for n? Yes; n=1Yes; n=2Yes; n=3No
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In my kitchen there are 3 ceiling lights and 4 wall switches. Here's the deal: Each switch controls 1 and only 1 light.Each light is controlled by at least one switch.When you enter the kitchen [you might not want to open the fridge] you find the switches positioned randomly up or down.Your mission, should you choose to accept it, is to determine how the lights and switches are connected.You may [repeatedly, but using the same value of n each time] simultaneously change any n [0 < n < 4] of the switches and note what happens. If you want to minimize the number of times you execute Step 5 above, is there a preferred value of n? You might want to think of the lights as A, B and C; the switches as 1, 2, 3 and 4.
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The puzzle does on this forum. Three cards: black-black, black-white, white-white. Same question; page__view__findpost__p__6216. Two thirds. In comparing total and favorable outcomes, it's rather easy to forget about equal likelihood. If that happens, we become unalterably certain of an incorrect result. A simple, outrageous example asks: how many lottery tickets must I buy in order to have a 50% chance of winning? The obvious answer is, only one ticket! Why is it so clear that only one ticket is needed? There are only two outcomes; one of them is favorable.
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Kudos to plainglazed for finding one-third of the answer. Note to DeeGee: one always declares the higher ranking of two possible hands. See the 2nd spoiler in this post. You would never call 4 Aces 2 pairs, for example. Here are three clues to get us through the entire puzzle.
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This has been posted and solved at least twice, in different settings, and Searching for the previous posts is difficult owing to different settings for the puzzle. There are two solutions of interest - the one that gets the person to safety the quickest, and the one that keeps the greatest distance between the person and the danger. I posted the second solution, previously, but I can't find the reference. If anyone's interested, I can reproduce it. - bn
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The 52C5 = 2 598 960 poker hands without jokers have values inversely related to their frequency of occurrence: SF = . . . .40 - straight flush 4K = . . . 624 - 4 of a kind FH = . . 3 744 - full house FL = . . 5 108 - flush ST = . .10 200 - straight 3K = . .54 912 - 3 of a kind 2P = . 123 552 - 2 pair 1P = 1 098 240 - 1 pair HC = 1 302 540 - high card Jokers are wild cards: they can be counted as duplicating any other card in the deck. If a joker is added to the deck, does the order of precedence of the hands change? What if two jokers are added? With a wild card in the deck, a 10th hand: 5 of a kind, becomes possible. Whatever its frequency, its presence in the list does not affect the order of the other 9 hands. Thus in answering the puzzle, ignore the relative frequency of 5OAK, and consider only the relative values of the original 9 hands.
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There is an easy solution
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Yes.
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There are more.
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Put a cork in it [original thread]
bonanova replied to bonanova's question in New Logic/Math Puzzles
The shape must pass completely through each of the holes. Your cube will not pass through either the circular or triangular holes. Consider them to be hole in a wall separating two rooms. The shape must pass from one room to the other, in turn, through all three holes, fitting each hole snugly as it passes. There are actually an infinity of 3-dimensional solids that will do this. One has a largest and another has a smallest volume. What are these volumes? Refer to the figure in the for dimensions of the holes. The circle has a 2" diameter; the square and triangle have 2" sides. Since this puzzle asks a new question, it's fair game to look at the answers given there. -
Nice.
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Clarifying: How many different polygons can be made by slicing a cube with a plane? No one has it, yet.
