Brain Teasers and Maths Puzzles
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 mistergreen77
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Brain Teasers and Maths Puzzles
Rules: Don't include the answer straight away. Allow at least five more posts before submitting the answer. This is to give someone a chance to post the answer thus stealing your glory. If five more brain teasers or spam posts are posted then you can post your answer.
This first one is a paradox of algebra, a proof that 1 + 1 = 1. Can you find the fault with this proof. I am using ^ to stand for squared.
a = b
a^ = ab
a^  b^ = ab  b^
(a+b)(ab) = b(ab)
a + b = b
Now if a = 1 then 1 + 1 = 1.
This first one is a paradox of algebra, a proof that 1 + 1 = 1. Can you find the fault with this proof. I am using ^ to stand for squared.
a = b
a^ = ab
a^  b^ = ab  b^
(a+b)(ab) = b(ab)
a + b = b
Now if a = 1 then 1 + 1 = 1.
[size=84][color=green]“Everything should be made as simple as possible, but not one bit simpler.”[/color]  Einstein
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
it's very simple
but I visit a spezial mathschool... I think we 've learnd such things in the seventh grade like every other schhool (in germany)
You have to think only more practically as theoreticallly (the grammar is incorect, isn't it )
In my opinion it's a very nice idea for a thread thanx mistergreen
but I visit a spezial mathschool... I think we 've learnd such things in the seventh grade like every other schhool (in germany)
You have to think only more practically as theoreticallly (the grammar is incorect, isn't it )
In my opinion it's a very nice idea for a thread thanx mistergreen
> It's a hundred and six miles to Chicago. We've got a full tank of gas, half a pack of cigarettes, it's dark, and we're wearing sunglasses.
 mistergreen77
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 Posts: 269
 Joined: Fri Mar 31, 2006 2:09
 Location: Brisbane
Thats okay mariesa  feel free to steal my glory by submitting the answer before I do (in about four posts time). Do you have any puzzles or teasers for us? In the meantime, here is another:
In our currency we have the following coins. 5c , 10c, 50c, $1.00, $2.00.
I am holding two coins in my hand, the value of which combines to 70c. But one of them is not a 50c piece. What two coins am I holding?
In our currency we have the following coins. 5c , 10c, 50c, $1.00, $2.00.
I am holding two coins in my hand, the value of which combines to 70c. But one of them is not a 50c piece. What two coins am I holding?
[size=84][color=green]“Everything should be made as simple as possible, but not one bit simpler.”[/color]  Einstein
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
 Chroelle
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 Location: Location, location...
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Okay. Here is one I got almost a year ago as an SMS, and it bothered me the entire day...
SGSW, Chillum and Tinoco walks to the marketplace bar to buy a keg of beer. They buy one for 30 Kroner (Danish currency) and pay 10 kroner each. After they leave Dizi suddenly realises that the keg was on sale for 25 kroner, and being the honest person she is, she asks Raillo to find them and pay them back the 5 kroner. He gets five ones and goes on his way. Raillo gets to keep the 2 oners, as the three guys could divide it fairly between them, so they get a oner each.
SGSW, Chillum and Tinoco now payd 9 kroner each for the bottle, which adds up to 27 kroner, and Raillo has the two oners he got for finding them.
27+2= 29
Where did that last krone go???
SGSW, Chillum and Tinoco walks to the marketplace bar to buy a keg of beer. They buy one for 30 Kroner (Danish currency) and pay 10 kroner each. After they leave Dizi suddenly realises that the keg was on sale for 25 kroner, and being the honest person she is, she asks Raillo to find them and pay them back the 5 kroner. He gets five ones and goes on his way. Raillo gets to keep the 2 oners, as the three guys could divide it fairly between them, so they get a oner each.
SGSW, Chillum and Tinoco now payd 9 kroner each for the bottle, which adds up to 27 kroner, and Raillo has the two oners he got for finding them.
27+2= 29
Where did that last krone go???
Currently testing Life version 2.9 (With added second child)
(Beta testing in progress)
www.paedit.dk  My blog in Danish
Clothes make the man. Naked people have little or no influence on society.
Mark Twain
(Beta testing in progress)
www.paedit.dk  My blog in Danish
Clothes make the man. Naked people have little or no influence on society.
Mark Twain
Re: Brain Teasers and Maths Puzzles
a = b, therefore ab = 0; division by zero occurs.mistergreen77 wrote:This first one is a paradox of algebra, a proof that 1 + 1 = 1. Can you find the fault with this proof. I am using ^ to stand for squared.
a = b
a^ = ab
a^  b^ = ab  b^
(a+b)(ab) = b(ab)
a + b = b
Now if a = 1 then 1 + 1 = 1.
This one is a classic:
At the end of the universe, there's a hotel with infinite number of rooms. However, just as expected with my luck, the only time I've ended up straying that far from home, the receptionist of that very same hotel informs me all the rooms are currently taken thanks to some intergalactical peace conference taking place in the hotel.
"Shucks", I say frustrated and turn to leave, when the receptionist interrupts me and says, "Just a minute sir; I did say we're fully booked, but there's still something we can do in order to find you an accomodation in this modest hotel of ours."
"Huh? And what is that?", I ask sounding surprised naturally. Well, what could be done?
 mistergreen77
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 Joined: Fri Mar 31, 2006 2:09
 Location: Brisbane
The beer did not cost 27 kroner. It cost 25 plus the 2 fee they paid railo for bringing their change making 27. So the equation is not 3x9+2=27 because that is counting the money paid to Railo twice and ignoring the change they received. Instead it shold be 25 + 3 + 2 = 30. Can anyone explain this better?
Thanks Chroelle, I hadn't seen that once since I was very young and I had to really think about it. And congratulions to pitkin for getting mine  division by zero is the error. I don't have a clue about Pitkin's puzzle though it has me intrigued.
Thanks Chroelle, I hadn't seen that once since I was very young and I had to really think about it. And congratulions to pitkin for getting mine  division by zero is the error. I don't have a clue about Pitkin's puzzle though it has me intrigued.
[size=84][color=green]“Everything should be made as simple as possible, but not one bit simpler.”[/color]  Einstein
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
 Chroelle
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 Posts: 9870
 Joined: Fri Feb 17, 2006 9:19
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Well since infinity can not really be filled up, there seems to be some weirdness going on, as they say all rooms are booked. So if there really is an infinite number of rooms, there will be room for you to, and the next infinite number of people that should want accomodation....
Currently testing Life version 2.9 (With added second child)
(Beta testing in progress)
www.paedit.dk  My blog in Danish
Clothes make the man. Naked people have little or no influence on society.
Mark Twain
(Beta testing in progress)
www.paedit.dk  My blog in Danish
Clothes make the man. Naked people have little or no influence on society.
Mark Twain
Then the answer has sth to do with maths...and if mariesa is close...
Let's try that way. The number of rooms is infinite, so n means actually the same as n + 1. The number of people is finite, so the receptionist could say to everyone "please move to the next room" and then room no. 1 will be free...
Another solution: Pitkin moves at once to room no. n + 1
Second solution is better I think, imagine poor receptionist girl calling almost infinite number of people only to free one room... As a gentleman I cant go for this solution.
Let's try that way. The number of rooms is infinite, so n means actually the same as n + 1. The number of people is finite, so the receptionist could say to everyone "please move to the next room" and then room no. 1 will be free...
Another solution: Pitkin moves at once to room no. n + 1
Second solution is better I think, imagine poor receptionist girl calling almost infinite number of people only to free one room... As a gentleman I cant go for this solution.
"As you have noticed over the years, we are not angry people." (itebygur)
alright  I'm going to try one as well
This was given by my math teacher at some point during sixth form  it's purely math so some might find it extremely easy  other's difficult as hell
the rectangle in the corner is 8 cm long and 4 cm broad  task is now to find the length of the radius of the circle
This was given by my math teacher at some point during sixth form  it's purely math so some might find it extremely easy  other's difficult as hell
the rectangle in the corner is 8 cm long and 4 cm broad  task is now to find the length of the radius of the circle
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They say that it takes a second to meet a special person
An hour to appreciate her
A day to love her
But an entire life to forget her
Never to be forgotten
An hour to appreciate her
A day to love her
But an entire life to forget her
Never to be forgotten
 mistergreen77
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 Posts: 269
 Joined: Fri Mar 31, 2006 2:09
 Location: Brisbane
The answer to this one is a 50c and a 20c piece. This is logically consistent with 'one of them is not a 50c piece'.In our currency we have the following coins. 5c , 10c, 50c, $1.00, $2.00.
I am holding two coins in my hand, the value of which combines to 70c. But one of them is not a 50c piece. What two coins am I holding?
Guybrush has me stumped at this stage though.
[size=84][color=green]“Everything should be made as simple as possible, but not one bit simpler.”[/color]  Einstein
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
 mistergreen77
 Tycoon
 Posts: 269
 Joined: Fri Mar 31, 2006 2:09
 Location: Brisbane
A right angled triangle with the radius as the hypotenuse will have sides of r4 and r8 so using pythagoras theorem (^ for squared)
(r8)^ + (r4)^ = r^
My algebra is a bit rusty though and I can't remember how to solve it.
Here is another:
Peter rabbit runs around the sides of an equilateral triangle at a constant speed without stopping. The first leg takes 80 seconds, and so does the second, but it takes 1min 20 seconds to complete the third side! Can you explain?
(r8)^ + (r4)^ = r^
My algebra is a bit rusty though and I can't remember how to solve it.
Here is another:
Peter rabbit runs around the sides of an equilateral triangle at a constant speed without stopping. The first leg takes 80 seconds, and so does the second, but it takes 1min 20 seconds to complete the third side! Can you explain?
[size=84][color=green]“Everything should be made as simple as possible, but not one bit simpler.”[/color]  Einstein
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
[color=green]“There is always some madness in love. But there is also always some reason in madness.”[/color]  Nietzsche[/size]
:twisted: [url=http://forum.connectwebdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]
 Chroelle
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 Posts: 9870
 Joined: Fri Feb 17, 2006 9:19
 Location: Location, location...
 Contact:
Well I knew yours MRGREEN. But since you did not include a 20c coin in your currency I found it rather hard to calculate...
BTW: How do you figure out what the smilie squared is...
BTW: How do you figure out what the smilie squared is...
Currently testing Life version 2.9 (With added second child)
(Beta testing in progress)
www.paedit.dk  My blog in Danish
Clothes make the man. Naked people have little or no influence on society.
Mark Twain
(Beta testing in progress)
www.paedit.dk  My blog in Danish
Clothes make the man. Naked people have little or no influence on society.
Mark Twain
I wondered and wondered and than : how mean !!! it's really trickymistergreen77 wrote:
Peter rabbit runs around the sides of an equilateral triangle at a constant speed without stopping. The first leg takes 80 seconds, and so does the second, but it takes 1min 20 seconds to complete the third side! Can you explain?
> It's a hundred and six miles to Chicago. We've got a full tank of gas, half a pack of cigarettes, it's dark, and we're wearing sunglasses.
right you are mistergreen
I did not notice the small fact that it's difficult to solve such an equation without slightly advanced calculators so the method you proposed is fine  the answer will be 20 cm  other answer will be 4, but for obvious reasons that is a false answer
I did not notice the small fact that it's difficult to solve such an equation without slightly advanced calculators so the method you proposed is fine  the answer will be 20 cm  other answer will be 4, but for obvious reasons that is a false answer
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 circle2.JPG (18.23 KiB) Viewed 8360 times
They say that it takes a second to meet a special person
An hour to appreciate her
A day to love her
But an entire life to forget her
Never to be forgotten
An hour to appreciate her
A day to love her
But an entire life to forget her
Never to be forgotten