Miscellaneous Combinatorial Puzzles 171- A GENERAL ELECTION
In how many different ways maya Parliament of 615 members be elected
if there are only four parties: Conservatives, Liberals, Socialists, and In-
dependents? You see you might have C. 310, L. 152, S. 150, I. 3; or C. 0, L. 0,
S. 0, I. 615; or C. 205, L. 205, S. 205, I. 0; and so on. The candidates are in-
distinguishable, as we are only concerned with the party numbers.
- THE MAGISTERIAL BENCH
A friend at Singapore asked me some time ago to give him my solution to
this problem. A bench of magistrates (he does not say where) consists of two
Englishmen, two Scotsmen, two Welshmen, one Frenchman, one Italian, one
Spaniard, and one American. The Englishmen will not sit beside one another,
the Scotsmen will not sit beside one another, and the Welshmen also object
to sitting together.
In how many different ways may the ten men sit in a straight line so that
no two men of the same nationality shall ever be next to one another?- CROSSING THE FERRY
Six persons, all related, have to cross a river in a small boat that will only
hold two. Mr. Webster, who had to plan the little affair, had quarrelled with
his father-in-law and his son, and, I am sorry to say, Mrs. Webster was not
on speaking terms with her own mother or her daughter-in-law. In fact, the
relations were so strained that it was not safe to permit any of the belligerents
to pass over together or to remain together on the same side of the river. And
to prevent further discord, no man was to be left with two women or
two men with three women.
How are they to perform the feat in the fewest possible crossings? No
tricks, such as making use of a rope or current, or swimming across, are
allowed.
- MISSIONARIES AND CANNIBALS
There is a strange story of three missionaries and three cannibals, who had
to cross a river in a small boat that would only carry two men at a time.