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athos20145
Topic Author
Posts: 96
Joined: July 14th, 2002, 3:00 am

### I can't solve this ...

... 3 people go to a restaurant. They eat and the bill amounts to 30 euros. They decide to share the bill so they pay 10 euros each. The restaurant owner gives them a discount of 5 euros, and he returns 5 euros in 1 euro coins. The 3 diners decide to take 1 euro each, so spending 9 euros each, and they leave a tip of 2 euros to the waiter. The diners spent 9 euros times 3 = 27 euros plus 2 euros tip for a total of 29 euros. Where has the missing euro gone?

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: I can't solve this ...

There's no missing Euro because the total is NOT 27+2. Instead it's 27 put in by the diners of which the restaurant took 25, leaving 2 for the waiter.

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: I can't solve this ...

This is the stuff Gödel was taking about, it's unsolvable.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: I can't solve this ...

And Douglas Adams showed that it could be the basis for interstellar travel using Bistromathics.

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: I can't solve this ...

Lol, I must have read past that! Bistromathics

Cuchulainn
Posts: 61185
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: I can't solve this ...

Try doing the same exercise with 20% included.
http://www.datasimfinancial.com
http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

katastrofa
Posts: 8772
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: I can't solve this ...

... 3 people go to a restaurant. They eat and the bill amounts to 30 euros. They decide to share the bill so they pay 10 euros each. The restaurant owner gives them a discount of 5 euros, and he returns 5 euros in 1 euro coins. The 3 diners decide to take 1 euro each, so spending 9 euros each, and they leave a tip of 2 euros to the waiter. The diners spent 9 euros times 3 = 27 euros plus 2 euros tip for a total of 29 euros. Where has the missing euro gone?
The ultimate proof that Italians don't get on well with the Euro.

athos20145
Topic Author
Posts: 96
Joined: July 14th, 2002, 3:00 am

### Re: I can't solve this ...

There's no missing Euro because the total is NOT 27+2.  Instead it's 27 put in by the diners of which the restaurant took 25, leaving 2 for the waiter.
Absolutely!

athos20145
Topic Author
Posts: 96
Joined: July 14th, 2002, 3:00 am

### Re: I can't solve this ...

... 3 people go to a restaurant. They eat and the bill amounts to 30 euros. They decide to share the bill so they pay 10 euros each. The restaurant owner gives them a discount of 5 euros, and he returns 5 euros in 1 euro coins. The 3 diners decide to take 1 euro each, so spending 9 euros each, and they leave a tip of 2 euros to the waiter. The diners spent 9 euros times 3 = 27 euros plus 2 euros tip for a total of 29 euros. Where has the missing euro gone?
The ultimate proof that Italians don't get on well with the Euro.
lol

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: I can't solve this ...

What's the area of this triangle?

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: I can't solve this ...

What's the area of this triangle?
LOL!

Do you need that to 100 digits?

wileysw
Posts: 593
Joined: December 9th, 2006, 6:13 pm

### Re: I can't solve this ...

this problem is due to Vladimir I. Arnold, who claimed that he had seen it in a standard American examination and used it as an example to criticize American math education.

such triangle does not exist.  one way to see it is that the vertex of the right angle lies on a circle with the hypotenuse as a diameter, thus the corresponding altitude is at most half of the hypotenuse, which is 5 in this case.

this of course assumes Euclidean geometry.  it's not difficult to embed such triangle into e.g., a 2-sphere, though it would be beyond Arnold's point as he was referring to children from age 5 to 15.

Cuchulainn
Posts: 61185
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: I can't solve this ...

What's the area of this triangle?
which one? There's 3 of them!
http://www.datasimfinancial.com
http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

Paul
Posts: 10093
Joined: July 20th, 2001, 3:28 pm

### Re: I can't solve this ...

What else is there to do while queuing for bread other than to criticise American mathematics education?

(There are at least five.)

Cuchulainn
Posts: 61185
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: I can't solve this ...

Now I see one more!
http://www.datasimfinancial.com
http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

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