Brain Teasers and Maths Puzzles

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mistergreen77
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Brain Teasers and Maths Puzzles

Post by mistergreen77 » Wed May 17, 2006 14:36

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)(a-b) = b(a-b)
a + b = b

Now if a = 1 then 1 + 1 = 1.
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Post by mariesa » Wed May 17, 2006 17:35

it's very simple :D :D :D

but I visit a spezial math-school... I think we 've learnd such things in the seventh grade :D :D :D like every other schhool (in germany)

You have to think only more practically as theoreticallly (the grammar is incorect, isn't it :D :D :D)

In my opinion it's a very nice idea for a thread :D 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.

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Post by mistergreen77 » Thu May 18, 2006 1:52

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?
[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.connect-webdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]

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Post by Chroelle » Thu May 18, 2006 10:41

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???
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Re: Brain Teasers and Maths Puzzles

Post by Pitkin » Thu May 18, 2006 13:44

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)(a-b) = b(a-b)
a + b = b

Now if a = 1 then 1 + 1 = 1.
a = b, therefore a-b = 0; division by zero occurs.


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?

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Post by mistergreen77 » Thu May 18, 2006 15:42

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.
[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.connect-webdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]

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Post by mariesa » Thu May 18, 2006 16:19

it isnt possible that a infinite number of rooms is fully booked, because infinit + 1 = infinite...
but I do not think that you've ment that .... or???
-> 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.

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Post by Pitkin » Thu May 18, 2006 16:20

You're not entirely wrong, mariesa-san. ;) The solution's not far; it's very close, actually.

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Post by Chroelle » Thu May 18, 2006 20:02

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....
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Post by eMTe » Thu May 18, 2006 20:13

And receptionist says: "Sir! You can take room no. "n"! Maybe that's the answer... :roll:
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Post by Pitkin » Thu May 18, 2006 20:30

I say mariesa-san is the closest to the 'classical answer' I'm looking for, but none of you are wrong here. :D

Hint: This demands some reorganizing and redistribution of rooms. All rooms (infinite) are booked, but the receptionist being the clever person s/he is knows how to deal with the situation.

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Post by eMTe » Thu May 18, 2006 20:56

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. :(
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Post by mariesa » Thu May 18, 2006 21:31

first solution sounds good :D
-> 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.

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Post by Pitkin » Thu May 18, 2006 22:10

The first solution was the one I was looking for, eMTe-san. And of course the hotel has a loudspeaker system, so that the poor receptionist doesn't have to call every customer separately. ;)

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Post by Guybrush » Thu May 18, 2006 22:32

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
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Post by mistergreen77 » Fri May 19, 2006 0:50

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?
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'.

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.connect-webdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]

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Post by mistergreen77 » Fri May 19, 2006 3:01

A right angled triangle with the radius as the hypotenuse will have sides of r-4 and r-8 so using pythagoras theorem (^ for squared)

(r-8)^ + (r-4)^ = 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.connect-webdesign.dk/viewtopic.php?p=5411#5411]Society of Sinister Minds.[/url]

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Post by Chroelle » Fri May 19, 2006 8:48

Well I knew yours MRGREEN. But since you did not include a 20c coin in your currency I found it rather hard to calculate... :rolleyes:

BTW: How do you figure out what the smilie squared is... :lol:
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Post by mariesa » Fri May 19, 2006 9:30

mistergreen77 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?
I wondered and wondered and than : how mean !!! it's really tricky :wink: :D :wink:
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Post by Guybrush » Fri May 19, 2006 9:55

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
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