A very short examination of this puzzle game should convince the reader
that Hendrick can never catch the black hog, and that the white hog can
never be caught by Katruen.
Each hog merely runs in and out of one of the nearest corners and can
never be captured. The fact is, curious as it must at first sight appear,
a Dutchman cannot catch a black hog, and a Dutchwoman can never capture a
white one! But each can, without difficulty, catch one of the other
colour.
So if the first player just determines that he will send Hendrick after
the white porker and Katruen after the black one, he will have no
difficulty whatever in securing both in a very few moves.
It is, in fact, so easy that there is no necessity whatever to give the
line of play. We thus, by means of the game, solve the puzzle in real
life, why the Dutchman and his wife could not catch their pigs: in their
simplicity and ignorance of the peculiarities of Dutch hogs, each went
after the wrong animal.
The little principle involved in this puzzle is that known to
chess-players as "getting the opposition." The rule, in the case of my
puzzle (where the moves resemble rook moves in chess, with the added
condition that the rook may only move to an adjoining square), is simply
this. Where the number of squares on the same row, between the man or
woman and the hog, is odd, the hog can never be captured; where the
number of squares is even, a capture is possible. The number of squares
between Hendrick and the black hog, and between Katruen and the white hog,
is 1 (an odd number), therefore these individuals cannot catch the
animals they are facing. But the number between Hendrick and the white
hog, and between Katruen and the black one, is 6 (an even number),
therefore they may easily capture those behind them.