. Eden.

The Problem is to prove that there must be, every day, at least _one_
married couple who are not in the same party.

pg192
6.

After the six friends, named in Problem 5, had returned from their tour,
three of them, Barry, Cole, and Dix, agreed, with two other friends of
theirs, Lang and Mill, that the five should meet, every day, at a
certain _table d'hote_. Remembering how much amusement they had derived
from their code of rules for walking-parties, they devised the following
rules to be observed whenever beef appeared on the table:--

(1) If Barry takes salt, then either Cole or Lang takes _one_ only of
the two condiments, salt and mustard: if he takes mustard, then either
Dix takes neither condiment, or Mill takes both.

(2) If Cole takes salt, then either Barry takes only _one_ condiment, or
Mill takes neither: if he takes mustard, then either Dix or Lang takes
both.

(3) If Dix takes salt, then either Barry takes neither condiment or Cole
take both: if he takes mustard, then either Lang or Mill takes neither.

(4) If Lang takes salt, then Barry or Dix takes only _one_ condiment: if
he takes mustard, then either Cole or Mill takes neither.

(5) If Mill takes salt, then either Barry or Lang takes both condiments:
if he takes mustard, then either Cole or Dix takes only _one_.

The Problem is to discover whether these rules are _compatible_; and, if
so, what arrangements are possible.

[N.B. In this Problem, it is assumed that the phrase "if Barry
takes salt" allows of _two_ possible cases, viz. (1) "he takes
salt _only_"; (2) "he takes _both_ condiments". And so with all
similar phrases.

It is also assumed that the phrase "either Cole or Lang takes
_one_ only of the two condiments" allows _three_ possible cases,
viz. (1) "Cole takes _one_ only, Lang takes both or neither";
(2) "Cole takes both or neither, Lang takes _one_ only"; (3)
"Cole takes _one_ only, Lang takes _one_ only". And so with all
similar phrases.

It is also assumed that every rule is to be understood as
implying the words "and _vice versa_." Thus the first rule would
imply the addition "and, if either Cole or Lang takes only _one_
condiment, then Barry takes salt."]

pg193
7.

(1) Brothers, who are much admired, are apt to be self-consci