" that it is the highest number of rows obtainable.

22.--_The Franklin's Puzzle._

The answer to this puzzle is shown in the illustration, where the numbers
on the sixteen bottles all add up to 30 in the ten straight directions.
The trick consists in the fact that, although the six bottles (3, 5, 6,
9, 10, and 15) in which the flowers have been placed are not removed, yet
the sixteen need not occupy exactly the same position on the table as
before. The square is, in fact, formed one step further to the left.

[Illustration]

23.--_The Squire's Puzzle._

The portrait may be drawn in a single line because it contains only two
points at which an odd number of lines meet, but it is absolutely
necessary to begin at one of these points and end at the other. One point
is near the outer extremity of the King's left eye; the other is below it
on the left cheek.

24.--_The Friar's Puzzle._

The five hundred silver pennies might have been placed in the four bags,
in accordance with the stated conditions, in exactly 894,348 different
ways. If there had been a thousand coins there would be 7,049,112 ways.
It is a difficult problem in the partition of numbers. I have a single
formula for the solution of any number of coins in the case of four bags,
but it was extremely hard to construct, and the best method is to find
the twelve separate formulas for the different congruences to the modulus
12.

25.--_The Parson's Puzzle._

[Illustration]

A very little examination of the original drawing will have shown the
reader that, as he will have at first read the conditions, the puzzle is
quite impossible of solution. We have therefore to look for some
loophole in the actual conditions as they were worded. If the Parson
could get round the source of the river, he could then cross every bridge
once and once only on his way to church, as shown in the annexed
illustration. That this was not prohibited we shall soon find. Though the
plan showed all the bridges in his parish, it only showed "part of" the
parish itself. It is not stated that the river did not take its rise in
the parish, and since it leads to the only possible solution, we must
assume that it did. The answer would be, therefore, as shown. It should
be noted that we are clearly prevented from considering the possibility
of getting round the mouth of the river, because we are told it "joined
the sea some hundred miles to the south," while no paris