EPT{3,7,9,11,13,17,19...491,493,497,499}=199 ways
Brainteasers/Math problems - Page 13
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gyth
657 Posts
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Murderotica
Vatican City State2594 Posts
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jaerak
United States124 Posts
+ Show Spoiler + Treat high templar as the number +1 and dark templar as -1. Multiply all of them templar together to get the type of templar left at the end. So odd # of dark templar --> dark templar at end. Even # of dark templar --> high templar at end. | ||
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JeeJee
Canada5652 Posts
On April 11 2011 06:34 MusicalPulse wrote: One that's similar to the liters of water problem. Here's what you have: -Two 8-liter jugs, filled with water -One 3-liter jug, empty -Four infinite size, empty pools Here's what your objective is: Fill each of the four pools with exactly 4 liters of water. ----- i assume you can't just take 8 and split into 4-4 using equal water levels as that would make the problem trivial that said, it's still trivial, i never understood how these are riddles. i just go into it and start pouring willy nilly, knowing that it'll solve itself at some point.. here's the solution i came up with + Show Spoiler + 8-8-0:0-0-0-0 8-5-3:0-0-0-0 8-5-0:3-0-0-0 8-2-3:3-0-0-0 8-0-0:3-2-3-0 8-0-2:3-0-3-0 7-0-3:3-0-3-0 7-3-0:3-0-3-0 4-3-3:3-0-3-0 0-3-3:3-4-3-0 0-8-3:0-4-1-0 0-8-0:0-4-4-0 0-5-3:0-4-4-0 0-0-0:5-4-4-3 0-0-3:2-4-4-3 0-3-3:2-1-4-3 0-6-0:2-1-4-3 0-8-0:2-1-4-1 0-5-3:2-1-4-1 0-5-0:2-1-4-4 0-2-3:2-1-4-4 0-2-0:2-4-4-4 0-0-0:4-4-4-4 | ||
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JeeJee
Canada5652 Posts
On April 11 2011 06:54 Murderotica wrote: + Show Spoiler + Fill 3, put in 8 (3), fill 3, put in 8 (6). Fill 3, put in 8 (3), fill 3, put in 8 (6). Pour 8a (6) in 8b (6) -> 8a (4), 8b (8) Pour 8a into one of the infinite pools. Repeat 3 times after emptying jugs. this doesn't work btw edit: re the stars question this immediately popped into my head if you haven't seen her videos i encourage you to. if you're a nerd that is | ||
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Murderotica
Vatican City State2594 Posts
Oh I didn't see there wasn't infinite water. fixed: + Show Spoiler + 8a 8b 3 Pa Pb Pc Pd 8 8 0 0 0 0 0 8 5 3 0 0 0 0 8 0 3 5 0 0 0 8 3 0 5 0 0 0 8 3 3 2 0 0 0 8 3 0 2 3 0 0 5 3 3 2 3 0 0 5 3 0 2 6 0 0 2 3 3 2 6 0 0 0 3 3 4 6 0 0 0 6 0 4 6 0 0 0 0 0 4 12 0 0 0 8 0 4 4 0 0 0 5 3 4 4 0 0 0 0 3 4 4 5 0 0 3 0 4 4 5 0 0 3 3 4 4 2 0 0 6 0 4 4 2 0 0 6 3 4 1 2 0 0 8 1 4 1 2 0 0 8 0 4 1 2 1 0 5 3 4 1 2 1 0 5 0 4 4 2 1 0 2 3 4 4 2 1 0 0 3 4 4 4 1 0 0 0 4 4 4 4 | ||
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Tintti
Finland46 Posts
On April 11 2011 06:10 gyth wrote: The difference between you being able to only hold 7 facts in your mind versus there only being 7 facts in the whole universe. If it was a limit on his mind + Show Spoiler + then the last thing he'd know is that he couldn't know everything. + Show Spoiler + Ah yes, I implicitly assumed that a person may actually know everything there is to know. | ||
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pikagrue
79 Posts
You have place 1001 unit squares on a coordinate plane. The squares can overlap (any number of squares can overlap in any fashion). Prove that the minimum amount of area where an odd number of squares overlap (amount of area covered by an odd number of squares) is equal to 1. The sides of the squares are parallel to the X and Y axes This has a really nice 1-2 line solution. EDIT: Single layer counts as an odd number btw. | ||
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Aequos
Canada606 Posts
On April 11 2011 07:15 pikagrue wrote: Why my math thing no on front page?! T___T You have place 1001 unit squares on a coordinate plane. The squares can overlap (any number of squares can overlap in any fashion). Prove that the minimum amount of area where an odd number of squares overlap (amount of area covered by an odd number of squares) is equal to 1. The sides of the squares are parallel to the X and Y axes This has a really nice 1-2 line solution. To clarify yours - is the overlap between an odd number of squares all added together (for example, if I overlap them in such a way that they resemble a Venn Diagram, do the mergers between 1 and 2, 2 and 3, and 1 and 3 add to the merger of 1, 2, and 3 to form the area covered? | ||
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Housemd
United States1407 Posts
+ Show Spoiler + There are now 32 black squares and 30 white squares and each domino always covers two neighboring squares. The neighboring squares are always opposite in color. Due to this, the first 30 dominoes on the board must cover the 30 white squares and 30 black squares. You will then have one domino remaining. However there will be two black squares remaining. One domino only covers two opposite color squares so therefore it will not be able to cover the chess board. | ||
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Murderotica
Vatican City State2594 Posts
On April 11 2011 07:15 pikagrue wrote: Why my math thing no on front page?! T___T You have place 1001 unit squares on a coordinate plane. The squares can overlap (any number of squares can overlap in any fashion). Prove that the minimum amount of area where an odd number of squares overlap (amount of area covered by an odd number of squares) is equal to 1. The sides of the squares are parallel to the X and Y axes This has a really nice 1-2 line solution. They would just be stacked on top of each other, not adding to the initial area of 1. Because the overlap of multiple squares adds nothing to this area of one square, it is the minimum area of overlap. Unless I misunderstood your question (why do they HAVE to overlap, if you are asking about the net minimum area of overlap? why an odd number of squares, it seems irrelevant to my solution?). | ||
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pikagrue
79 Posts
On April 11 2011 07:42 Murderotica wrote: They would just be stacked on top of each other, not adding to the initial area of 1. Because the overlap of multiple squares adds nothing to this area of one square, it is the minimum area of overlap. Unless I misunderstood your question (why do they HAVE to overlap, if you are asking about the net minimum area of overlap? why an odd number of squares, it seems irrelevant to my solution?). I'm asking you to prove that there is no way to place the 1001 squares such that the area covered by an odd number of squares (see picture below) is less than 1. If you notice, if you overlap 2 squares on top of eachother, they cancel eachother's areas out. On April 11 2011 07:23 Aequos wrote: To clarify yours - is the overlap between an odd number of squares all added together (for example, if I overlap them in such a way that they resemble a Venn Diagram, do the mergers between 1 and 2, 2 and 3, and 1 and 3 add to the merger of 1, 2, and 3 to form the area covered? I'll draw a picture (mspaint ftw) ![[image loading]](http://i.imgur.com/UlB9z.png) I made it circles instead of squares because it's easier to draw. The total area that would count would be the red, blue, yellow, (all covered by 1 circle) and black (covered by 3 circles) parts. The orange, green, and purple parts would not count, because they are covered by 2 circles each. | ||
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Housemd
United States1407 Posts
To start off, a truel is exactly like a duel just with three people. One morning Mr. Black, Mr. Gray, and Mr. White decide to resolve a dispute by trueling with pistols until only one of them survives. Mr. Black is the worst shot, hitting once every three times (1/3). Mr. Gray is the second best shot, hitting his target twice out of every three times (2/3). Lastly, Mr. White always hits his target (1/1). To make it fair, Mr. Black will shot first, following by Mr. Gray (if he is still alive) and then Mr. White (provided that he is still alive). The Question is: Where should Mr. Black aim his first shot? | ||
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gyth
657 Posts
ABCD 388 Can you take the water out of the pools once you pour it in? Doesn't seem reasonable for "infinite" pools, not that infinite pools are reasonable (or in any way necessary for the problem?) P.S. you can use [ code ] [ /code ] tags to monospace your answers | ||
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Murderotica
Vatican City State2594 Posts
On April 11 2011 07:43 pikagrue wrote: I'm asking you to prove that there is no way to place the 1001 squares such that the area covered by an odd number of squares (see picture below) is less than 1. If you notice, if you overlap 2 squares on top of eachother, they cancel eachother's areas out. I'll draw a picture (mspaint ftw) I made it circles instead of squares because it's easier to draw. The total area that would count would be the red, blue, yellow, (all covered by 1 circle) and black (covered by 3 circles) parts. The orange, green, and purple parts would not count, because they are covered by 2 circles each. Um so lets say I put 999 squares in a grid of 9 x 111, then in the top right corner of this grid I put one square that overlaps with the corner square by say .1 area, then one right on top of that one. So there are 3 squares overlapping an area of .1, 2 squares overlapping an area of .9 (which doesn't matter since they cancel their area out [wtf do you mean by that btw]), and the rest of the squares are not overlapping. Would that not defy the premise? | ||
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gyth
657 Posts
Um so lets say I put 999 squares in a grid of 9 x 111, then in the top right corner of this grid I put one square that overlaps with the corner square by say .1 area, then one right on top of that one. So there are 3 squares overlapping an area of .1, 2 squares overlapping an area of .9 (which doesn't matter since they cancel their area out [wtf do you mean by that btw]), and the rest of the squares are not overlapping. Would that not defy the premise? The ones not overlapping would be a single layer, ie an odd number. | ||
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gyth
657 Posts
http://www.techinterviewpuzzles.com/2010/06/warden-and-23-prisoners-google.html The answer given seems rather odd, I'd rather have the leader count to 23 than 44. | ||
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Murderotica
Vatican City State2594 Posts
On April 11 2011 07:45 Housemd wrote: Okay, I think I'll add one that isn't on the thread. To start off, a truel is exactly like a duel just with three people. One morning Mr. Black, Mr. Gray, and Mr. White decide to resolve a dispute by trueling with pistols until only one of them survives. Mr. Black is the worst shot, hitting once every three times (1/3). Mr. Gray is the second best shot, hitting his target twice out of every three times (2/3). Lastly, Mr. White always hits his target (1/1). To make it fair, Mr. Black will shot first, following by Mr. Gray (if he is still alive) and then Mr. White (provided that he is still alive). The Question is: Where should Mr. Black aim his first shot? There is not a 50-50 chance that the guy you are shooting does not shoot you back if someone shot me I'd be dead certain to shoot that fucker back. + Show Spoiler + However If Black kills White then he has a 2/3 chance of dying. If he doesn't then he has a 0 chance of dying, Gray will shoot white next. If White is still alive, he will shoot Gray. If White is dead, Black will shoot Gray. If Black kills Gray then he has a 1 chance of dying. If he doesn't then he has a 0 chance of dying, Gray will shoot White next. If White is still alive, he will shoot Gray. If White is dead, Black will shoot Gray. It's pretty obvious that Black wants Gray alive as long as possible, because Gray shoot White and White will kill Gray on his first shot, so it's more profitable for him to shoot White. | ||
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Murderotica
Vatican City State2594 Posts
On April 11 2011 08:02 gyth wrote: The ones not overlapping would be a single layer, ie an odd number. So why does a grid of squares that do not overlap at all not work? The area of overlap in this case is 0. | ||
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Murderotica
Vatican City State2594 Posts
On April 11 2011 07:45 gyth wrote: 4-pool.+ Show Spoiler + ABCD 388 Can you take the water out of the pools once you pour it in? Doesn't seem reasonable for "infinite" pools, not that infinite pools are reasonable (or in any way necessary for the problem?) P.S. you can use [ code ] [ /code ] tags to monospace your answers This is more elegant anyways. | ||
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