(related to Problem: The City Luncheons)
The men may be grouped as follows, where each line represents a day and each column a table:—
$$\begin{array}{cccccc}
AB&CD&EF&GH&IJ&KL\\
AE&DL&GK&FI&CB&HJ\\
AG&LJ&FH&KC&DE&IB\\
AF&JB&KI&HD&LG&CE\\
AK&BE&HC&IL&JF&DG\\
AH&EG&ID&CJ&BK&LF\\
AI&GF&CL&DB&EH&JK\\
AC&FK&DJ&LE&GI&BH\\
AD&KH&LB&JG&FC&EI\\
AL&HI&JE&BF&KD&GC\\
AJ&IC&BG&EK&HL&FD
\end{array}$$`
Note that in every column (except in the case of the$A$'s) all the letters descend cyclically in the same order,$B, E, G, F,$up to$J,$which is followed by$B.$`
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