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Subject: "1-1 corrrespondence"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #435
Reading Topic #435
Renee Lon
guest
Mar-27-04, 11:40 PM (EST)
 
"1-1 corrrespondence"
 
   I have been working on the poem the ten weary travelers. I believe that you use a 1-1 correspondence to solve it, but I am not sure I have it exactly right. The set of men 1-10 and the set of rooms A-I are not even so you drop the first guy to get a 1-1 correspondence. But then what? Still you end up with 9 guys in a room. What happens to the 10th?


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alexbadmin
Charter Member
1952 posts
Mar-27-04, 11:56 PM (EST)
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1. "RE: 1-1 corrrespondence"
In response to message #0
 
   >I have been working on the poem the ten weary travelers. I
>believe that you use a 1-1 correspondence to solve it, but I
>am not sure I have it exactly right. The set of men 1-10
>and the set of rooms A-I are not even so you drop the first
>guy to get a 1-1 correspondence.

Is it how the poem goes? Drop the first guy?

>But then what? Still you
>end up with 9 guys in a room.

If the memory serves, according to the poem, at no point in time there were 9 guys in one room. They've been waiting in the foyer to be assigned a room one at a time starting with the third one.

>What happens to the 10th?

First he accompanies B to room A. After the rest have been settled in rooms B-H, he is moved to room I.


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Pierre Charland
Member since Dec-22-05
Jan-27-07, 08:11 AM (EST)
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2. "RE: 1-1 corrrespondence"
In response to message #1
 
   By the way, here is the poem:
https://www.curiouser.co.uk/paradoxes/9rooms.htm

A 19th Century Paradoxical Poem.

Ten weary, footsore travellers,
All in a woeful plight,
Sought shelter at a wayside inn
One dark and stormy night.

'Nine rooms, no more,' the landlord said
'Have I to offer you.
To each of eight a single bed,
But the ninth must serve for two.'

A din arose. The troubled host
Could only scratch his head,
For of those tired men not two
Would occupy one bed.

The puzzled host was soon at ease -
He was a clever man -
And so to please his guests devised
This most ingeneous plan.

In a room marked A two men were placed,
The third was lodged in B,
The fourth to C was then assigned,
The fifth retired to D.

In E the sixth he tucked away,
In F the sventh man.
The eighth and ninth in G and H,
And then to A he ran,

Wherein the host, as I have said,
Had laid two travellers by;
Then taking one - the tenth and last -
He logged him safe in I.

Nine singe rooms - a room for each -
Were made to serve for ten;
And this it is that puzzles me
And many wiser men.

This poem appeared in Current Literature, vol 2, April 1889. No author was credited.

This ninth stanza exposing the fallacy was sent to Martin Gardner by John F. Mooney...

If we reflect on what he's done,
We'll see were not insane.
Two men in A he's counted one,
Not once but once again.

AlphaChapMtl


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alexbadmin
Charter Member
1952 posts
Jan-28-07, 06:51 PM (EST)
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3. "RE: 1-1 corrrespondence"
In response to message #2
 
   Many thanks for taking the time.

Alex


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