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The Coffee Shop

  • Thread starter The Fallen Angel
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After a recount Velut Luna has taken the lead with 22 points. Sympazero is falling back and Eulalia is running out of steam. Into the final stretch and it's nip and tuck between Velut and Wragg....this could go either way.
 
And the solution is
Crucified,cider,cred,cried,crud,crude,curd,cure,cured,curie,dicier,dire,ecru,fire,fired,fried,icier,rice,riced,ride,rife,rude,rued and uric.
Our gold medal goes to Velut Luna with silver to Wragg and bronze to Eulalia.
Next up I believe is a puzzle from Sympazero so get thinking caps ready!!
 
melissa said:
And the solution is
Crucified,cider,cred,cried,crud,crude,curd,cure,cured,curie,dicier,dire,ecru,fire,fired,fried,icier,rice,riced,ride,rife,rude,rued and uric.
Our gold medal goes to Velut Luna with silver to Wragg and bronze to Eulalia.
Next up I believe is a puzzle from Sympazero so get thinking caps ready!!
Click to expand...

Here’s a brain-teaser for the kaffee klatsch:

Three traveling salesmen find a cheap hotel for the night.
The desk clerk checks them into a $30 room.
They each hand over $10 then go up to the room to sleep.

Later the night manager comes on and realizes the salesmen have been overcharged – it’s not a $30 room, but only a $25 room. And since there’s a rumor of a hotel inspector in the neighborhood he decides to play it safe and refund $5.

He summons the bellboy, gives him five singles and instructs him to go upstairs and refund the $5 to the salesmen.

On the way upstairs the bellboy figures the salesmen won’t be any wiser if he takes a cut, so he pockets two of the five singles, knocks on the door and gives the salesmen the other three dollars.

The three salesmen are happy; they each paid $10 and now each have $1 change and so have only paid $9 each for the room.
Now here’s the problem: Three times $9 equals $27 – plus the two dollars in the bellboy’s pocket makes $29. Where’s the 30th dollar?

(If you know the solution please keep it to yourself, and let the others figure it out.)
 
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melissa said:
And the solution is
Crucified,cider,cred,cried,crud,crude,curd,cure,cured,curie,dicier,dire,ecru,fire,fired,fried,icier,rice,riced,ride,rife,rude,rued and uric.
Our gold medal goes to Velut Luna with silver to Wragg and bronze to Eulalia.
Next up I believe is a puzzle from Sympazero so get thinking caps ready!!
Click to expand...
Very well done Luna, and well done Wragg - this slavegirl's happy to kneel in her lowly place.
One word which I confirmed was in the Concise Oxford Dict was 'dicer', one who plays dice - isn't that in Chambers?
 
Dicer is not in the official solution list so it's still Italy leading the medal table table with one gold. The second gold medal is now up for grabs and will be awarded to the first correct solution. I do know the answer to this problem set by Sympazero2 and it can be difficult to explain.
 
sympazero2 said:
Here’s a brain-teaser for the kaffee klatsch:

Three traveling salesmen find a cheap hotel for the night.
The desk clerk checks them into a $30 room.
They each hand over $10 then go up to the room to sleep.

Later the night manager comes on and realizes the salesmen have been overcharged – it’s not a $30 room, but only a $25 room. And since there’s a rumor of a hotel inspector in the neighborhood he decides to play it safe and refund $5.

He summons the bellboy, gives him five singles and instructs him to go upstairs and refund the $5 to the salesmen.

On the way upstairs the bellboy figures the salesmen won’t be any wiser if he takes a cut, so he pockets two of the five singles, knocks on the door and gives the salesmen the other three dollars.

The three salesmen are happy; they each paid $10 and now each have $1 change and so have only paid $9 each for the room.
Now here’s the problem: Three times $9 equals $27 – plus the two dollars in the bellboy’s pocket makes $29. Where’s the 30th dollar?

(If you know the solution please keep it to yourself, and let the others figure it out.)
Click to expand...
Pp has heard this as each handing over $10 to pay for a $25 meal. He knows the secret but will not tell.
 
The really difficult thing about the problem is explaining exactly why the logic of adding $27 and $2 in an attempt to make $30 is wrong. So far I have received two attempts so there will be three medals on offer for the best explanations.
 
sympazero2 said:
Here’s a brain-teaser for the kaffee klatsch:

Three traveling salesmen find a cheap hotel for the night.
The desk clerk checks them into a $30 room.
They each hand over $10 then go up to the room to sleep.

Later the night manager comes on and realizes the salesmen have been overcharged – it’s not a $30 room, but only a $25 room. And since there’s a rumor of a hotel inspector in the neighborhood he decides to play it safe and refund $5.

He summons the bellboy, gives him five singles and instructs him to go upstairs and refund the $5 to the salesmen.

On the way upstairs the bellboy figures the salesmen won’t be any wiser if he takes a cut, so he pockets two of the five singles, knocks on the door and gives the salesmen the other three dollars.

The three salesmen are happy; they each paid $10 and now each have $1 change and so have only paid $9 each for the room.
Now here’s the problem: Three times $9 equals $27 – plus the two dollars in the bellboy’s pocket makes $29. Where’s the 30th dollar?

(If you know the solution please keep it to yourself, and let the others figure it out.)
Click to expand...
The travelers have paid only $ 30.
They got $ 3. Thus, each paid $ 9. 3x9 is 27. 27 plus the three received back dollars 30th
The hotel owner has not cashed $ 27, but only 25. The two missing, the service person.
 
madiosi said:
The travelers have paid only $ 30.
They got $ 3. Thus, each paid $ 9. 3x9 is 27. 27 plus the three received back dollars 30th
The hotel owner has not cashed $ 27, but only 25. The two missing, the service person.
Click to expand...
Not quite what Pp thinks......
 
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Best solutions received




Wragg's explanation


The question is simply trying to confuse the reader by suggesting that adding the bellboy’s ill gotten gains to the $27 that they coughed up should make $30. But three nines are $27 plus the $3 that they got back makes $30,the wastrel bellboy and his sticky fingers don’t enter into that equation – his thieving ways robbed them of paying $25 instead of $27 for their room.
I reckon the bellboy went to Cruxton Grange prep school.

Velut Luna's solution

Excuse me but Sympa is a little devil ! Forget all before!
the right equation is:
25 + 2 + 3 = 30; i.e. 25 + 2 = 30 - 3
They actually pay 27$ the price of the chamber 25$ plus the robbed 2$.
Now for the balance you have to ADD the 3$ of refund not the 2$ robbed (this is the Sympa trick
For the balance you have to add 3$ and not as Sympa tell 2$!
If you change the position of a term in an equation from one part of '=' to the other you have to change the - in + , and viceversa.
The equation is not:
(9x3)+2 = 29 ;
but (8.333 x 3) = 25 , the real price;
2 the robbed dollars;
25 + 2 = 27 = 9 x 3 , the actually payed price;
3 the refund;
27 + 3 = 30 $
and not to count the 2 robbed dollars for two times as Sympa tell! i.e. 25 +2 +2 =29

Primus Pilus

Don't have time for a detailled explanation but, in reality, you need to break down to whom the money is actually paid.

Each guest pays $8.33 to the hotel for the room (not $9) and $0.66 to the bellhop.

3 x $8.33 = $25
3 x $0.66 = $2

This actually does leave 3 cents missing but no one really notices that.

And from Madiosi

The travelers have paid only $ 30.
They got $ 3. Thus, each paid $ 9. 3x9 is 27. 27 plus the three received back dollars 30th
The hotel owner has not cashed $ 27, but only 25. The two missing, the service person.

The medals are awarded as follows

In joint Gold position we have Wragg and Velut Luna.
Wragg's explanation is correct, short and to the point. Velut Luna's explanation is excellent and is the only one who introduces some algebra and mentions that the 2 dollars is counted twice. Luna did go astray in previous attempts however but still deserves gold for a full explanation.

Madiosi is also correct and in silver position..lacks a detailed explanation,

Similarly PP...but is still worthy of a bronze.

At the heart of the illusion is the fact that the men did pay out a total of 3x9 = 27 dollars...that is TRUE. If you then add the 2 dollars in the bellboy's pocket that makes 29 dollars which creates the impression that a dollar is missing! There is no mathematical reason why the 27 and 2 should be added together!! Try the same problem with different numbers and you will see what I mean.

Well done to all contestants and Sympazero2 for the problem. Italy is now clearly in the lead in the medals table but it is good to see Team GB with our first gold.

I must give advance warning that the next problem...should you attempt a solution will have you seriously doubting your sanity...more later.
 
melissa said:
Best solutions received




Wragg's explanation


The question is simply trying to confuse the reader by suggesting that adding the bellboy’s ill gotten gains to the $27 that they coughed up should make $30. But three nines are $27 plus the $3 that they got back makes $30,the wastrel bellboy and his sticky fingers don’t enter into that equation – his thieving ways robbed them of paying $25 instead of $27 for their room.
I reckon the bellboy went to Cruxton Grange prep school.

Velut Luna's solution

Excuse me but Sympa is a little devil ! Forget all before!
the right equation is:
25 + 2 + 3 = 30; i.e. 25 + 2 = 30 - 3
They actually pay 27$ the price of the chamber 25$ plus the robbed 2$.
Now for the balance you have to ADD the 3$ of refund not the 2$ robbed (this is the Sympa trick
For the balance you have to add 3$ and not as Sympa tell 2$!
If you change the position of a term in an equation from one part of '=' to the other you have to change the - in + , and viceversa.
The equation is not:
(9x3)+2 = 29 ;
but (8.333 x 3) = 25 , the real price;
2 the robbed dollars;
25 + 2 = 27 = 9 x 3 , the actually payed price;
3 the refund;
27 + 3 = 30 $
and not to count the 2 robbed dollars for two times as Sympa tell! i.e. 25 +2 +2 =29

Primus Pilus

Don't have time for a detailled explanation but, in reality, you need to break down to whom the money is actually paid.

Each guest pays $8.33 to the hotel for the room (not $9) and $0.66 to the bellhop.

3 x $8.33 = $25
3 x $0.66 = $2

This actually does leave 3 cents missing but no one really notices that.

And from Madiosi

The travelers have paid only $ 30.
They got $ 3. Thus, each paid $ 9. 3x9 is 27. 27 plus the three received back dollars 30th
The hotel owner has not cashed $ 27, but only 25. The two missing, the service person.

The medals are awarded as follows

In joint Gold position we have Wragg and Velut Luna.
Wragg's explanation is correct, short and to the point. Velut Luna's explanation is excellent and is the only one who introduces some algebra and mentions that the 2 dollars is counted twice. Luna did go astray in previous attempts however but still deserves gold for a full explanation.

Madiosi is also correct and in silver position..lacks a detailed explanation,

Similarly PP...but is still worthy of a bronze.

At the heart of the illusion is the fact that the men did pay out a total of 3x9 = 27 dollars...that is TRUE. If you then add the 2 dollars in the bellboy's pocket that makes 29 dollars which creates the impression that a dollar is missing! There is no mathematical reason why the 27 and 2 should be added together!! Try the same problem with different numbers and you will see what I mean.

Well done to all contestants and Sympazero2 for the problem. Italy is now clearly in the lead in the medals table but it is good to see Team GB with our first gold.

I must give advance warning that the next problem...should you attempt a solution will have you seriously doubting your sanity...more later.
Click to expand...

The simpler and shorter answer:
The solution to this mathematical problem is that there IS no solution.

The narrative is carefully constructed to mislead and confuse. The reality is you cannot express a mathematical problem which contains addition, subtraction, multiplication and division in random order and expect a logical conclusion.

Try this: Hold up your left hand, spread the fingers then proceed to count them backwards "Ten, nine, eight, seven six..." Then hold up your right hand and say "...plus five makes eleven."(It greatly amuses children)

And that, friends, is the same basic trick as the Salesmen and the missing dollar.
It's just as easy to create one missing dollar as it is one extra finger.

S
 
sympazero2 said:
The simpler and shorter answer:
The solution to this mathematical problem is that there IS no solution.

The narrative is carefully constructed to mislead and confuse. The reality is you cannot express a mathematical problem which contains addition, subtraction, multiplication and division in random order and expect a logical conclusion.

Try this: Hold up your left hand, spread the fingers then proceed to count them backwards "Ten, nine, eight, seven six..." Then hold up your right hand and say "...plus five makes eleven."(It greatly amuses children)

And that, friends, is the same basic trick as the Salesmen and the missing dollar.
It's just as easy to create one missing dollar as it is one extra finger.

S
Click to expand...
Pp and his R&D colleagues have oft pondered this condundrum while trying to apportion restaurant bills late at night after 1 or 2 too many red wines and far, far too many nightcaps. We always come back to a mathematical solution based on apportioning the bill between two variables:
X = the number of corporate credit cards available and
Y = the number of taxationally appropriate guests whether visible or invisible
He will share his mathematical solution with you off-line when he has a computer with the appropriate mathematical symbols.
 
The Algebra Test

ANYONE ATTEMPTING A SOLUTION TO THIS PROBLEM DO SO AT THEIR OWN RISK.

Every working day, Mon to Fri I have the same maths class in the morning. At the end of the lesson on Friday I announced that there would be an algebra test one day next week but my students would not know exactly which day until I handed the papers out.
“So, it's going to be a surprise test then is it miss?” said Connie. I agreed that yes, it must come as a surprise to them.
Tree put Ulrika down and casually observed to the class that “It can't be Friday then.” “Why not?” asked Ulrika adjusting her knickers. “Because if it is then we would know by Thursday afternoon. After all if Mon, Tues, Wed and Thu mornings have all passed by without a test then a Friday test cannot be a surprise.” replied Tree assuming his usual cool posture.
I listened with some concern. Just then I overheard Velut Luna say that this means that the test must be one of the days from Monday to Thursday...and that if it is on Thursday then we would know that by Wednesday afternoon. We know that Friday is ruled out and if Mon, Tues and Wed have passed by then only Thursday remains so we cannot have a surprise test on Thursday.
My concern was deepening. I had spent ages preparing the test papers. Barbaria piped up “Thanks to Tree and Velut we can rule out Friday and Thursday but we can also rule out Wednesday!..because if we haven't had a test by Tuesday afternoon then we'll know it must be on Wednesday!..no surprise then no test!”
RR and Little Siss in unison pointed out that by a similar argument it could not be on Tuesday either. PP then concluded that the test must be on Monday.
“But wait a minute!!” exploded Eulalia. “We all now know that the test is on Monday so it cannot come as a surprise!” “No surprise then no test!” piped up Wragg.
All my students decided not to study and had a brilliant weekend. I didn't. I sat at home and glared at the test papers in an envelope on my desk. How could I their maths teacher be defeated by such simple logic!
Monday came and went with the unused test papers still in my bag. The students all carried huge grins. Tuesday morning arrived. Same class, same grins, same envelope glaring at me from my bag. I was defeated and all knew it. Suddenly I grabbed the envelope and opened it!! “SILENCE!! You are now going to have your surprise algebra test. DO NOT turn over the test paper until I tell you to.” I ordered.
The shock wave could have been felt half way round the globe. “But...but...you can't!!” they protested. Tree dropped Ulrika to the floor, mouth open, eyes glazed. “Oh yes I can!!” I gloated. I stormed up and down each aisle handing out test papers like they were individual death sentences. I gloried in my moment of triumph. I had defied all logic and given them a surprise test.

So.....where did my students' logic go wrong?

This is an open problem so please post your solutions here. You can find fault with others' arguments. Medals will be awarded for the quality of logic used.
 
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My:
Imagine we have two balls in a bag, one black and one white, once you remove the black will do the test, once you remove the white one we'll be safe, in any day of the week we will not be sure which ball we can extract, the odds are only two, or black or white. Only after the extraction of Thursday we will know, if for four times we were so lucky enough to pull out the white ball, which on Friday will be the test. Before the event is random and does not restrict the probability that there is, or there is not, the test.
 
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