he 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.

79.--_The Thirty-one Game._

By leading with a 5 the first player can always win. If your opponent
plays another 5, you play a 2 and score 12. Then as often as he plays a 5
you play a 2, and if at any stage he drops out of the series, 3, 10, 17,
24, 31, you step in and win. If after your lead of 5 he plays anything
but another 5, you make 10 or 17 and win. The first player may also win
by leading a 1 or a 2, but the play is complicated. It is, however, well
worth the reader's study.

80.--_The Chinese Railways._

This puzzle was artfully devised by the yellow man. It is not a matter
for wonder that the representatives of the five countries interested were
bewildered. It would have puzzled the engineers a good deal to construct
those circuitous routes so that the various trains might run with safety.
Diagram 1 shows directions for the five systems of lines, so that no line
shall ever cross another, and this appears to be the method that would
require the shortest possible mileage.

[Illustration]

The reader may wish to know how many different solutions there are to the
puzzle. To this I should answer that the number is indeterminate, and I
will explain why. If we simply consider the case of line A alone, then
one route would be Diagram 2, another 3, another 4, and another 5. If 3
is different from 2, as it undoubtedly is, then we must regard 5 as
different from 4. But a glance at the four diagrams,