[Illustration]
An entertaining little puzzle with cards is to take the nine cards of a
suit, from ace to nine inclusive, and arrange them in the form of the
letter "T," as shown in the illustration, so that the pips in the
horizontal line shall count the same as those in the column. In the
example given they add up twenty-three both ways. Now, it is quite easy
to get a single correct arrangement. The puzzle is to discover in just
how many different ways it may be done. Though the number is high, the
solution is not really difficult if we attack the puzzle in the right
manner. The reverse way obtained by reflecting the illustration in a
mirror we will not count as different, but all other changes in the
relative positions of the cards will here count. How many different ways
are there?