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Quiz of the Month (August 2001)
Hector C. Parr
***
SOLUTION TO LAST MONTH'S QUIZ
1). 2 minutes.
2). 35 degrees.
3). 13.
Notes
1). In one minute the hot tap provides 1/6 of a bathful, and
the cold tap provides 1/3. So together they provide
1/6 + 1/3 = 1/2. So time to fill bath equals 2 minutes.
2). The cold tap provides twice as much water as the hot. So
the temperature divides the interval 15 to 75 in the
ratio 1:2. So temperature is 15 + 60/3 = 35 degrees.
3). Each time water is added the strength of the whisky is
reduced by a factor of 0.95. Now 0.95^{13} = 0.5133,
and 0.95^{14} = 0.4877. So water may be added 13
times before strength becomes less that 0.5.

THIS MONTH'S QUIZ
1. Three married couples are to sit down for dinner at a
circular table. In how many ways can they occupy the
six chairs if the men and women are to sit alternately?
2. In how many ways can they occupy the six chairs if the
men and women sit alternately, and no man sits next to
his wife?
3. Four married couples are to sit down for dinner at a
circular table. In how many ways can they occupy the
eight chairs if they sit alternately with no man next
to his wife?

***
(c) Hector C. Parr (2001)
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