## THE CITY LUNCHEONS.

(

Combination and Group Problems)

Twelve men connected with a large firm in the City of London sit down to

luncheon together every day in the same room. The tables are small ones

that only accommodate two persons at the same time. Can you show how

these twelve men may lunch together on eleven days in pairs, so that no

two of them shall ever sit twice together? We will represent the men by

the first twelve letters of the alphabet, and suppose the first day's

pairing to be as follows--

(A B) (C D) (E F) (G H) (I J) (K L).

Then give any pairing you like for the next day, say--

(A C) (B D) (E G) (F H) (I K) (J L),

and so on, until you have completed your eleven lines, with no pair ever

occurring twice. There are a good many different arrangements possible.

Try to find one of them.

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