nine rooms paradox
A puzzle that was first published in Current Literature vol. 2,
April 1889. It takes the form of a poem:
Ten weary, footsore travellers,
How has the host managed to bamboozle his patrons? This puzzle is similar
to that of the missing dollar.
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 ingenious 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 seventh 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.
One of the two customers who is initially placed in room A, whom we may
refer to as the "first" customer, is later transferred to room I and treated
as if he were also the "tenth" customer.