or 9 geese, leaving
24); he next sold Ned Collier a fifth of what he had left and gave him a
fifth of a goose "for the missus" (that is, 4-4/5 + 1/5 or 5 geese,
leaving 19). He then took these 19 back to his master.

58.--_The Chalked Numbers._

This little jest on the part of Major Trenchard is another trick puzzle,
and the face of the roguish boy on the extreme right, with the figure 9
on his back, showed clearly that he was in the secret, whatever that
secret might be. I have no doubt (bearing in mind the Major's hint as to
the numbers being "properly regarded") that his answer was that depicted
in the illustration, where boy No. 9 stands on his head and so converts
his number into 6. This makes the total 36--an even number--and by making
boys 3 and 4 change places with 7 and 8, we get 1278 and 5346, the
figures of which, in each case, add up to 18. There are just three other
ways in which the boys may be grouped: 1368--2457, 1467--2358, and
2367--1458.

59.--_Tasting the Plum Puddings._

The diagram will show how this puzzle is to be solved. It is the only way
within the conditions laid down. Starting at the pudding with holly at
the top left-hand corner, we strike out all the puddings in twenty-one
straight strokes, taste the steaming hot pudding at the end of the tenth
stroke, and end at the second sprig of holly.

Here we have an example of a chess rook's path that is not re-entrant,
but between two squares that are at the greatest possible distance from
one another. For if it were desired to move, under the condition of
visiting every square once and once only, from one corner square to the
other corner square on the same diagonal, the feat is impossible.

There are a good many different routes for passing from one sprig of holly
to the other in the smallest possible number of moves--twenty-one--but I
have not counted them. I have recorded fourteen of these, and possibly
there are more. Any one of these would serve our purpose, except for the
condition that the tenth stroke shall end at the steaming hot pudding.
This was introduced to stop a plurality of solutions--called by the maker
of chess problems "cooks." I am not aware of more than one solution to
this puzzle; but as I may not have recorded all the tours, I cannot make a
positive statement on the point at the time of writing.

[Illustration]

60.--_Under the Mistletoe Bough._

Everybody was found to have kissed everybody else o