Enigma 302: The Grand Enigma
13 August 2015
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From New Scientist #1450, 4th April 1985 [link]
The Puzzlers’ Union has just finished electing a new Grand Enigma, as its union president is called. Hook, Line and Sinker were the three candidates. Each canvassed shamelessly, and each arrived at the count expecting to receive 79 votes. As the total possible number of votes cast was, in fact, precisely 100, each was in for a surprise.
The Puzzlers’ Union has eight branches, all of different sizes and none of less than three members. Each branch made whatever promises it saw fit and, indeed, cast its votes en bloc. But, you may rightly infer, not all branches voted as promised. One branch had rashly pledged itself to all three candidates and then voted for no one. Three branches were pledged to two candidates — a different two in each case — and resolved the dilemma by voting for a third. This manoeuvre benefited Hook most, Line next and Sinker least. One branch promised no one and voted for no one. The remaining three branches were pledged one to Hook, one to Line and one to Sinker; and these pledges were kept in the vote.
Precisely how many votes did each candidate actually receive?
In New Scientist #1454 the following correction to this puzzle was published (I’ve removed the statement of the solution):
Martin Hollis writes: “As set, the puzzle has several solutions. In the first paragraph, 100 should have been given not as the total number of votes cast, but as the total possible. […] My apologies to all.”
I have modified the puzzle above accordingly.