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secondorder
Amanda Hug'n'kiss



Registered: 04/05/15
Posts: 532
Loc: Queensland, Australia
Last seen: 9 months, 6 days
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$31.63?
Which means that it was switched to $63.31
Minus the 5c newspaper that comes to $63.26, which is exactly double the original amount.
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Sun King



Registered: 02/15/14
Posts: 4,069
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Re: mathematical brain teaser thread [Re: secondorder]
#21936344 - 07/13/15 08:14 AM (8 years, 6 months ago) |
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Show your work.
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: Sun King]
#21936384 - 07/13/15 08:31 AM (8 years, 6 months ago) |
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Quote:
Sun King said: Show your work.
-------------------- Vi Veri Universum Vivus Vici
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secondorder
Amanda Hug'n'kiss



Registered: 04/05/15
Posts: 532
Loc: Queensland, Australia
Last seen: 9 months, 6 days
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I literally just guessed a random number in my head, it didn't work, so I kept moving it higher or lower depending on how close I was to ending up with double.
My thought process went something like:
What about $10.20, but $20.05 is less than double the original number. What about $20.40, nope, then I'm left with $40.15, which is even further from double. Okay, we want the resulting dollar number to be bigger, so why don't I increase the number of cents, and see if that gets me any closer: $20.41, that would give me $41.15, but that's more than double the original number. But, due to the doubling effect, the number of cents in the original number gets closer to the target number faster than the number of dollars does, which means I just need to go higher. $25.51 would leave me with $51.20, almost, only 18c off, but not quite, let's go higher. $30.61 would leave me with $61.25, only 3c off, that's so close so let's go up a bit slower now: $32.65 would give me $65.27, shit now I'm over by 3c, so it must be the number of dollars in between, which is $31.63, that gives me $63.26, perfect!
Or is the guess and check method not allowed?
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tryptkaloids
Learner



Registered: 02/08/15
Posts: 12,641
Loc: Exact Center
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Re: mathematical brain teaser thread [Re: secondorder]
#21936741 - 07/13/15 10:42 AM (8 years, 6 months ago) |
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if it takes 5 roaches to roll a joint how many joints can you roll with 25 roaches?
-------------------- "Remember, kids, the difference between science and screwing around is writing it down" -adam savage Flowchart for Recommended plan of action. Learn the tried and true way to grow mushrooms Use the Damn search engine After you know what you're doing, take a break Pick a book, Make some chips! Josex said:Don't take the site seriously bro, ain't worth it.
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Sun King



Registered: 02/15/14
Posts: 4,069
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Re: mathematical brain teaser thread [Re: tryptkaloids]
#21936766 - 07/13/15 10:52 AM (8 years, 6 months ago) |
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6 cause you can roll 5 then you have 5 more roaches to roll one more.
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tryptkaloids
Learner



Registered: 02/08/15
Posts: 12,641
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Re: mathematical brain teaser thread [Re: Sun King]
#21936923 - 07/13/15 11:37 AM (8 years, 6 months ago) |
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-------------------- "Remember, kids, the difference between science and screwing around is writing it down" -adam savage Flowchart for Recommended plan of action. Learn the tried and true way to grow mushrooms Use the Damn search engine After you know what you're doing, take a break Pick a book, Make some chips! Josex said:Don't take the site seriously bro, ain't worth it.
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Sun King



Registered: 02/15/14
Posts: 4,069
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Re: mathematical brain teaser thread [Re: secondorder]
#21938206 - 07/13/15 04:56 PM (8 years, 6 months ago) |
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Quote:
secondorder said: I literally just guessed a random number in my head, it didn't work, so I kept moving it higher or lower depending on how close I was to ending up with double.
My thought process went something like:
What about $10.20, but $20.05 is less than double the original number. What about $20.40, nope, then I'm left with $40.15, which is even further from double. Okay, we want the resulting dollar number to be bigger, so why don't I increase the number of cents, and see if that gets me any closer: $20.41, that would give me $41.15, but that's more than double the original number. But, due to the doubling effect, the number of cents in the original number gets closer to the target number faster than the number of dollars does, which means I just need to go higher. $25.51 would leave me with $51.20, almost, only 18c off, but not quite, let's go higher. $30.61 would leave me with $61.25, only 3c off, that's so close so let's go up a bit slower now: $32.65 would give me $65.27, shit now I'm over by 3c, so it must be the number of dollars in between, which is $31.63, that gives me $63.26, perfect!
Or is the guess and check method not allowed?
No guessing.
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: secondorder]
#21938642 - 07/13/15 06:38 PM (8 years, 6 months ago) |
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Quote:
secondorder said: $31.63?
Which means that it was switched to $63.31
Minus the 5c newspaper that comes to $63.26, which is exactly double the original amount.
This is in fact correct. A more rigorous approach to a solution than guess-and-check would be the following:
To determine the value of Brown's check, let x stand for the dollars and y stand for the cents. The problem can now be expressed by the following equation: 100y + x - 5 = 2(100x + y). This reduces to 98y - 199x = 5, a Diophantine equation with an infinite number of integral solutions. Only one solution, however, meets the problem's condition that the value of y be less than 100. This solution is x = 31 and y = 63, making Brown's check $31.63.
-------------------- Vi Veri Universum Vivus Vici
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: Sun King]
#21938647 - 07/13/15 06:39 PM (8 years, 6 months ago) |
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And I would say in the future I would prefer, and it is more fun with
Quote:
Sun King said: No guessing. 
-------------------- Vi Veri Universum Vivus Vici
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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PROBLEM #15
Quote:
In this multiplication problem each P stands for a prime digit (2,3,5, or 7). Solve the problem. The answer is unique.
P P P P P ----------- P P P P P P P P -------------- P P P P P
-------------------- Vi Veri Universum Vivus Vici
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DieCommie

Registered: 12/11/03
Posts: 29,258
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Quote:
DividedQuantum said:
Quote:
secondorder said: $31.63?
Which means that it was switched to $63.31
Minus the 5c newspaper that comes to $63.26, which is exactly double the original amount.
This is in fact correct. A more rigorous approach to a solution than guess-and-check would be the following:
To determine the value of Brown's check, let x stand for the dollars and y stand for the cents. The problem can now be expressed by the following equation: 100y + x - 5 = 2(100x + y). This reduces to 98y - 199x = 5, a Diophantine equation with an infinite number of integral solutions. Only one solution, however, meets the problem's condition that the value of y be less than 100. This solution is x = 31 and y = 63, making Brown's check $31.63.
How is that solution different than guess and check?
I don't see the specific steps to find an integer solution less than 100 of the under-specified system of equations. 
The answer is found by guess and check. But of course that is often a real way, and sometimes only way, to solve a problem.
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Kurt
Thinker, blinker, writer, typer.

Registered: 11/26/14
Posts: 1,688
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Re: mathematical brain teaser thread [Re: DieCommie]
#21939016 - 07/13/15 08:09 PM (8 years, 6 months ago) |
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The relation of logic and symbolism to mathematics is interesting to consider. Loosely it's correlated to the art of using emoticons to express yourself in a fine way.
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secondorder
Amanda Hug'n'kiss



Registered: 04/05/15
Posts: 532
Loc: Queensland, Australia
Last seen: 9 months, 6 days
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Re: mathematical brain teaser thread [Re: Kurt]
#21939219 - 07/13/15 08:51 PM (8 years, 6 months ago) |
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Quote:
How is that solution different than guess and check?
I don't see the specific steps to find an integer solution less than 100 of the under-specified system of equations. 
The answer is found by guess and check. But of course that is often a real way, and sometimes only way, to solve a problem. 
I, too don't see how it's any different to a guess and check method, it just happens to look fancier..
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: secondorder]
#21939276 - 07/13/15 09:03 PM (8 years, 6 months ago) |
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Okay, so, guess and check works very well, and the right answer is all that matters. Obviously. But come on guys. I think where Sun King and I are coming from, or at least where I am coming from, is that it's a lot more fun to see an elegant mathematical solution worked out. This is for the purposes of fun, I needn't remind anyone. These are not real life math problems. They are brainteasers for fun. Just putting the answer up there with no math or logic, correct or not, is lame. I'm disappointed that I had to explain this.
-------------------- Vi Veri Universum Vivus Vici
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Quote:
DividedQuantum said: PROBLEM #15
Quote:
In this multiplication problem each P stands for a prime digit (2,3,5, or 7). Solve the problem. The answer is unique.
P P P P P ----------- P P P P P P P P -------------- P P P P P
-------------------- Vi Veri Universum Vivus Vici
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secondorder
Amanda Hug'n'kiss



Registered: 04/05/15
Posts: 532
Loc: Queensland, Australia
Last seen: 9 months, 6 days
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Who are you to tell us what is and what isn't fun? I really enjoyed coming up with that answer the way I did! Demanding an "elegant mathematical solution" immediately renders some people unable to participate, and as my fifth grade teacher once said "Exclusion is simply not on!". I'm not well trained in mathematics. I just like trying to figure out these answers for myself. I'm not good at picturing those equations you posted in my head, whereas I am good at guessing and checking, and thinking in my own ways in my head. Can't we just keep coming up with the answers in our own way? Or will that ruin all the fun you are having?
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: secondorder]
#21939344 - 07/13/15 09:17 PM (8 years, 6 months ago) |
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Look, nevermind.
This is beginning to be a much bigger deal than it ever should have been.
secondorder, please, by all means, solve the problems however you want to. In the future, it would be better if you provided your thought process with the final answer -- whatever it is. That will be more than acceptable, I assure you. Elegant mathematics are not necessary. They're nice, but they were never necessary. Showing how you got there is important, though.
No more!
-------------------- Vi Veri Universum Vivus Vici
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DividedQuantum
Outer Head


Registered: 12/06/13
Posts: 9,819
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Re: mathematical brain teaser thread [Re: secondorder]
#21939351 - 07/13/15 09:18 PM (8 years, 6 months ago) |
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Quote:
secondorder said: I literally just guessed a random number in my head, it didn't work, so I kept moving it higher or lower depending on how close I was to ending up with double.
My thought process went something like:
What about $10.20, but $20.05 is less than double the original number. What about $20.40, nope, then I'm left with $40.15, which is even further from double. Okay, we want the resulting dollar number to be bigger, so why don't I increase the number of cents, and see if that gets me any closer: $20.41, that would give me $41.15, but that's more than double the original number. But, due to the doubling effect, the number of cents in the original number gets closer to the target number faster than the number of dollars does, which means I just need to go higher. $25.51 would leave me with $51.20, almost, only 18c off, but not quite, let's go higher. $30.61 would leave me with $61.25, only 3c off, that's so close so let's go up a bit slower now: $32.65 would give me $65.27, shit now I'm over by 3c, so it must be the number of dollars in between, which is $31.63, that gives me $63.26, perfect!
Or is the guess and check method not allowed?
This is good.
-------------------- Vi Veri Universum Vivus Vici
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DieCommie

Registered: 12/11/03
Posts: 29,258
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Quote:
DividedQuantum said: Look, nevermind.
This is beginning to be a much bigger deal than it ever should have been.
secondorder, please, by all means, solve the problems however you want to. In the future, it would be better if you provided your thought process with the final answer -- whatever it is. That will be more than acceptable, I assure you. Elegant mathematics are not necessary. They're nice, but they were never necessary. Showing how you got there is important, though.
No more!
I'm still interested in the solution though...
Elegant or not, I thought that there might be some way to algorithmically solve the system with restraints of being an integer and being less than 100. I tried to solve it myself and quickly realized that there was not enough equations to solve for the variables. Does setting up the equation like the answer showed help guide in the guess and check?
edit - Let me dig in a little because I think you can take it... Quote:
Just putting the answer up there with no math or logic, correct or not, is lame.
Copying the answer from somewhere else without understanding enough to know that it lacks logic and math is lame.
Edited by DieCommie (07/13/15 10:54 PM)
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