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foreva.infiniti Regular user 6 Posts a + a 6 Posts = 116 Posts |
Anybody got any good 1s?
Here: Brothers and Sisters, I have none. But this man's father is my father's son.
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
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Herr Brian Tabor Special user Oklahoma City 729 Posts |
He is talking about his son.
What is higher without a head, than with a head? |
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tommy Eternal Order Devil's Island 16544 Posts |
What makes a son who drinks beer with no head tick?
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.
Tommy |
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landmark Inner circle within a triangle 5194 Posts |
There's a whole lot of puzzles in the "Puzzle me this" section, foreva, from the fairly easy to the really difficult.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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MobilityBundle Regular user Las Vegas/Boston 120 Posts |
Here's one. Hopefully it's not too much like a math problem.
Consider an unspecified number of spheres floating in otherwise-empty space. You can think of them as planets, but they're not moving relative to each other... no fancy orbital mechanics or anything like that. They're all the same size. Call a point on one of the planets "public" if there's a line of sight from that point to some other point on some other planet. Call a point "private" if it's not public. Just to illustrate the definition, suppose you have three planets in a line. All the points on the middle planet are public, because they can be seen by one of the two end planets. Similarly, only the outer half of each end planet is private. The inner halves are public, because those points can be seen by the middle planet. Okay, so the question: Suppose you have an unspecified number of planets, say n of them. A priori, the total private area will change based on how the planets are arranged in space. What is the maximum total private area? What is the minimum total private area? |
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ed rhodes Inner circle Rhode Island 2885 Posts |
*B-O-O-O-M!* - "I'm sorry. You've made Ed's head explode."
"...and if you're too afraid of goin' astray, you won't go anywhere." - Granny Weatherwax
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
The minimum sounds like the area of one planet.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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Pakar Ilusi Inner circle 5777 Posts |
What kind of thread needs no needle but can pop yo' brain?
This one.
"Dreams aren't a matter of Chance but a matter of Choice." -DC-
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landmark Inner circle within a triangle 5194 Posts |
Spheres same radius?
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
Quote:
On 2013-07-30 13:31, landmark wrote: Pretty much: Quote: On 2013-07-30 10:44, MobilityBundle wrote: |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
Quote:
On 2013-07-30 12:26, LobowolfXXX wrote: In fact, after a cursory inspection, it appears that the minimum and maximum are both the area of one planet. |
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
Quote:
On 2013-07-30 10:44, MobilityBundle wrote: For n=2 max private area=min private area =1/2 of total area. Howzat for a start?
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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landmark Inner circle within a triangle 5194 Posts |
Quote:
On 2013-07-30 13:54, S2000magician wrote: D'oh!!
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
Quote:
On 2013-07-30 13:58, Magnus Eisengrim wrote: Ditto for n = 3 (i.e., private area = area of one sphere). Thus, by induction, it's true for any n. ;) |
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MobilityBundle Regular user Las Vegas/Boston 120 Posts |
Quote:
On 2013-07-30 14:31, S2000magician wrote: Not a bad start! I'm not too sure about the induction step though. So, I admit, I posed the problem as deviously as it was posed to me. In fact, the maximum private area and the minimum private area are always the same, and are always equal to the area of a planet. There are, however, several proofs of the result. Some of them are very elementary... high school geometry, plus some creativity. Some of them are very elegant and sophisticated. I'll post details (or respond to private messages) for anyone who's interested. |
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MobilityBundle Regular user Las Vegas/Boston 120 Posts |
Okay, here's one a little less mathy, but it's a little wordy to state:
You're programming two "Mars rover" type of robots. They will each land on the same spherical planet. Assume the planet is featureless -- no distinguishing terrain; no oceans, rivers, canyons, or the like; no magnetic field by which to navigate, etc. Assume also that it has thick, uniform cloud coverage so one cannot see the external stars from the surface of the planet. Your goal is to program the robots (while they're still on Earth) so that after they land on the planet, they travel according to some path you come up with such that they are guaranteed to come within some small proximity of each other -- say, 1 meter. You don't know the robots' initial landing positions or orientations, but you do know the radius of the planet -- say, 10,000 km. (The actual distances of 10,000 km and 1 meter aren't important for the problem, but I've just stated them for definiteness.) You can assume the robots can travel over the entire surface of the planet, and they have sufficient fuel for an arbitrarily long journey. They also have proximity sensors that can determine whether they're within 1 meter of each other, and you have enough fuel to keep those sensors continually running. Each robot also has sensors sufficient to do dead reckoning -- meaning your program can have instructions along the lines of "turn so-and-so degrees" or "go forward for so-and-so distance." Each robot has sufficient memory to be able to return to any previous point of its trip, including its starting point. Each robot has sufficient processing power to compute direct paths between known points. Also, since you know the radius of the planet, you can have instructions like "go to the 'opposite' point from where I am now," where "opposite" means the point on the exact other side of the planet (like the North Pole / South Pole). Here's the kicker: the robots' programs must be identical. So, you can't have one robot wait where it landed while the other robot moves around and looks for it. You are allowed to generate random numbers in your program (for example, you can make the robots turn in a random direction or travel for a random distance), but assume that both robots will generate the same random number when executing that instruction. So, describe a path that guarantees the robots will get close to each other! And be prepared to justify why that path works, regardless of where the robots initially land and how they're initially pointing. |
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foreva.infiniti Regular user 6 Posts a + a 6 Posts = 116 Posts |
Mobility how are these brain teasers?
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
Quote:
On 2013-07-31 12:19, foreva.infiniti wrote: Why do you think they are not? To me, recreational mathematics is definitely part of the "brain teaser" genre.
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
Quote:
On 2013-07-31 11:45, MobilityBundle wrote: If they move in identical spirals - where the radius of the spiral increases by twice the proximity distance (2 meters, here) for each revolution - eventually they'll be close enough to say, "Howdy!" |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
Quote:
On 2013-07-30 14:53, MobilityBundle wrote: I'd have to ponder the case of n = 4, when the planets' centers aren't coplanar, for a proof. |
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