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Topic: ANSWERS TO MEDIUM PUZZLES!!! Part 1 (Read 10763 times) |
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I.M._Smarter_Enyu
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ANSWERS TO MEDIUM PUZZLES!!! Part 1
« on: Jul 26th, 2002, 9:34am » |
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RELATIVELY MEDIUM -- PART 1
RELATIVELY MEDIUM
>> GLOBE TRAVERSAL how many places are there on the earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere. also, the rotation of the earth has nothing to do with the solution; you can assume you're walking on a static sphere if that makes the problem less complicated to you. <<
Infinite number. Yes, the North Pole. AND, a ring near the South Pole, slightly more than 1 mile North of the South Pole, where after you go 1 mile South, you walk in a 1 mile circle totally around the South Pole, then North back to where you started.
>> GHETTO ENCRYPTION II Three coworkers would like to know their average salary. However, they are self-conscious and don't want to tell each other their own salaries, for fear of either being ridiculed or getting their houses robbed. How can they find their average salary, without disclosing their own salaries? <<
Person 1 receives the ones-place digit of everyone, adds them up, writes the answer down. Person 2 receives the tens-place digit of everyone, adds them up, writes the answer down. Etc. Then add up all the interim sums, divide by 3.
>> ADJACENCY GRID arrange the numbers 1 to 8 in the grid below such that adjacent numbers are not in adjacent boxes (horizontally, vertically, or diagonally). <<
Trick here is to recognize that 1 and 8 are special, as they only have 1 number adjacent. 1 is next to only 2, 8 is next to only 7, so you have to start off like this:
.X.
X1X
X8X
.X.
Now, there is only one place each for 2 and 7 to go:
.7.
X1X
X8X
.2.
The rest is trivial, here is one answer:
.7.
314
586
.2.
>> FAUSTIAN ROUND TABLE COIN GAME you die and the devil says he'll let you go to heaven if you beat him in a game. the devil sits you down at a round table. he gives himself and you a huge pile of quarters. he says "ok, we'll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. the first guy who can't put a quarter down loses." you guys are about to start playing, and the devil says that he'll go first. however, at this point you immediately interject, and ask if you can go first instead. you make this interjection because you are very smart, and you know that if you go first, you can guarantee victory. explain how you can guarantee victory. <<
You go in the exact center of the table, of course! Then wherever the devil goes, you go in the mirror-image location, on the opposite side of the quarter in the middle.
>> DOMINOES ON A CHESSBOARD using 31 dominoes, where one domino covers exactly two squares, can you cover all the empty squares on this chessboard (which has only 62 spaces, since two opposite corner squares are removed). if so, how? if not, why? prove your claim. <<
No you can't, imagine each domino is black on the left half and white on the right. To cover the 8x8 board, you'll need 32 dominoes, providing 32 black squares and 32 white squares. Now fill in the chess board with it's black and white colors. The removed corners are the same color, so you can't do it.
>> MANHOLES Why are manholes round? <<
Duh so the covers can't fall in the holes!
*** I.M. Smarter Enyu!!!
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Frothingslosh
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #1 on: Jul 26th, 2002, 1:32pm » |
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On FAUSTIAN ROUND TABLE COIN GAME
You made a slight but critical error. It's not the mirror image (which will fail),
you have to move to the exact 180 degree opposite location.
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mebden
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #2 on: Jul 27th, 2002, 11:14am » |
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The solution to Ghetto encryption won't work. Say person 'A' makes 23k per year, B makes 35k per year, and C makes 45k per year. And say B listens to the tens-of-thousands digit from A and C. Now he knows exactly who makes more than him, and who makes less! (2 < 3 < 4.) (Note that B knows that the tens-of-thousands digit is the largest possible one, after seeing the final average.)
A real solution is:
1. A thinks of a number, alpha. He averages his salary with that secret number and gives the result, beta, to B. B takes the result and averages his own salary with it, weighting beta twice as much. B then passes on his answer, gamma, to C. C averages his salary with gamma, weighting gamma twice as much. C passes the answer, delta, to A.
2. A then multiplies delta by 2, subtracts his magic number from the product, and finally, divides everything by 3. He announces the answer.
This way no one knows ANYTHING about anyone's salary, because right from the beginning it is all corrupted by A's secret number, which isn't cancelled out till the circle is complete.
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Pete Pete
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1 (Ghetto)
« Reply #3 on: Jul 27th, 2002, 11:54am » |
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For the salary averaging thing, just have them each dump a handful of pennis in a bag, one for each thousand they make. Dump out the bag and divide the pennies three ways.
I don't think Ghetto I is possible; without authentication, the courier could always do man-in-the-middle.
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Willis
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #4 on: Jul 30th, 2002, 5:36am » |
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Ghetto I is not so tricky.
Take your box, and lock it with one of your locks, and send it to your friend. Have him put one of his own locks on it, and then send it back to you. Remove your lock and send the box back to your friend. He can remove his lock and retrieve the contents. At no time during this exchange is the box unlocked and in transit.
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bartleby
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #5 on: Jul 30th, 2002, 10:06am » |
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on Jul 30th, 2002, 5:36am, Willis wrote:Ghetto I is not so tricky.
Take your box, and lock it with one of your locks, and send it to your friend. Have him put one of his own locks on it, and then send it back to you. Remove your lock and send the box back to your friend. He can remove his lock and retrieve the contents. At no time during this exchange is the box unlocked and in transit. |
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More importantly, no KEYS are ever sent! That sounds like it.
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Everend
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #6 on: Jul 30th, 2002, 11:33am » |
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Ghetto I
Just have your buddy send his lock to you, use it and dont' use any of your locks. (so you pay less shipping)
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Brion
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #7 on: Jul 30th, 2002, 3:49pm » |
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Sorry, both the last two Ghetto I solutions fail if you have a particularly evil interceptor.
Case 1: "Send your box with a lock, have your friend lock as well, take your lock off, friend takes lock off"
Fails if the interceptor puts his/her own lock on and sends the box back to you (never reaching your friend). You remove your lock thinking your friend has added theirs, and the interceptor can now remove his/her lock and get your treasure.
Case 2: "Have your friend send a lock and use it"
Fails for the same reason as #1: the interceptor grabs your friend's lock and exchanges it for one of his/her own. You use your "friend's" lock and when you send it back, the interceptor unlocks his/her locks and gets your goodies.
Cheers!
Brion
P.S. My solution is in a different topic.
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Robert Grimsley
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #8 on: Aug 23rd, 2002, 1:16pm » |
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See other threads regarding globe traversal and manholes.
Or, if you're too lazy:
>> Infinite number. Yes, the North Pole. AND, a ring near the South Pole, slightly more than 1 mile North of the South Pole, where after you go 1 mile South, you walk in a 1 mile circle totally around the South Pole, then North back to where you started.
This covers most of the answer, but you could also start out a bit closer to the south pole, such that your walk that circles totally around the south pole is only 1/2 mile in length, and you do it twice. This is another ring of answers, and if you do the circle walk 3 times, this is another rings of answers, and so forth.
As far as manholes, the no-drop theory seems plausible, but people that have researched it have come up with other reasons (historical, load-balancing, etc.). The covers and holes could be square as long as the size difference were sufficient, but this would cost more.
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pottymouthed
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Re: ANSWERS TO MEDIUM PUZZLES!!! Part 1
« Reply #9 on: Aug 30th, 2002, 4:59pm » |
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Re the Manhole covers....
My guess is the covers are round because the holes are round.
The holes are round because it's probably easy to drill a round hole than a square hole.
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