I once propounded the following puzzle in a London club, and for a
considerable period it absorbed the attention of the members. They could
make nothing of it, and considered it quite impossible of solution. And
yet, as I shall show, the answer is remarkably simple.
Two men are seated at a square-topped table. One places an ordinary
cigar (flat at one end, pointed at the other) on the table, then the
other does the same, and so on alternately, a condition being that no
cigar shall touch another. Which player should succeed in placing the
last cigar, assuming that they each will play in the best possible
manner? The size of the table top and the size of the cigar are not
given, but in order to exclude the ridiculous answer that the table
might be so diminutive as only to take one cigar, we will say that the
table must not be less than 2 feet square and the cigar not more than 4½
inches long. With those restrictions you may take any dimensions you
like. Of course we assume that all the cigars are exactly alike in
every respect. Should the first player, or the second player, win?