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Programming Enigma Puzzles

8 June 2022

Posted by on **From New Scientist #821, 23rd November 1972** [link]

With eight handsome bachelors and eight ravishing spinsters in the office, prospects look bright for matrimony. The snag is, however, all are fanatical Catholics or Protestants and the chances against a random bride and groom being of the same religion are nine to seven. In a random mixed marriage, the groom would probably not be a Catholic, even though there are more Catholic men than Protestant women.

How many of the 16 are Protestants?

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Odds of “nine to seven against” are a probability of 9/(9 + 7) = 9/16.

So of the 64 possible male/female pairs 9/16 of them (= 36) are mismatched (so 28 of them are matched).

If there are

xCatholic men andyProtestant women (sox > y), then the number of mismatched pairs is:And we are looking for

M= 36. (This is enough to find the answer to the puzzle).Additionally we are told that in a random mixed marriage (i.e. one of the 36 mismatched pairs) the groom would probably not be Catholic.

There are

xymismatched pairs with a Catholic groom, so we needxy< 18.Solution:There are 7 Protestants.We have 3 Catholic (and 5 Protestant) men, and 6 Catholic (and 2 Protestant) women.

There are 3×2 (= 6) mismatched pairs with a Catholic groom, and 5×6 (= 30) mismatched pairs with a Protestant groom.

So there are 36 mismatched pairs in total (as required) and fewer than half with a Catholic groom.