2936, 65281, 65983, and 86251.

Compare with the problems in "Digital Puzzles," section of _A. in M._,
and with Nos. 93 and 101 in these pages.

65.--_The Mystery of Ravensdene Park._

The diagrams show that there are two different ways in which the routes
of the various persons involved in the Ravensdene Mystery may be traced,
without any path ever crossing another. It depends whether the butler, E,
went to the north or the south of the gamekeeper's cottage, and the
gamekeeper, A, went to the south or the north of the hall. But it will be
found that the only persons who could have approached Mr. Cyril Hastings
without crossing a path were the butler, E, and the man, C. It was,
however, a fact that the butler retired to bed five minutes before
midnight, whereas Mr. Hastings did not leave his friend's house until
midnight. Therefore the criminal must have been the man who entered the
park at C.

[Illustration]

66.--_The Buried Treasure._

The field must have contained between 179 and 180 acres--to be more
exact, 179.37254 acres. Had the measurements been 3, 2, and 4 furlongs
respectively from successive corners, then the field would have been
209.70537 acres in area.

One method of solving this problem is as follows. Find the area of
triangle APB in terms of _x_, the side of the square. Double the
result=_xy_. Divide by _x_ and then square, and we have the value of
_y_^{2} in terms of _x_. Similarly find value of _z_^{2} in terms of _x_;
then solve the equation _y_^{2}+_z_^{2}=3^{2}, which will come out in the
form _x_^{4}-20_x_^{2}=-37. Therefore _x_^{2}=10+(sqrt{63})=17.937254
square furlongs, very nearly, and as there are ten acres in one square
furlong, this equals 179.37254 acres. If we take the negative root of the
equation, we get the area of the field as 20.62746 acres, in which case
the treasure would have been buried outside the field, as in Diagram 2.
But this solution is excluded by the condition that the treasure was
buried in the field. The words were, "The document ... states clearly
that the field is square, and that the treasure is buried in it."

[Illustration]

THE PROFESSOR'S PUZZLES

67.--_The Coinage Puzzle._

The point of this puzzle turns on the fact that if the magic square were
to be composed of whole numbers adding up 15 in all ways, the two must be
placed in one of the corners. Otherwise fractions must be used, and these
are supplied in the puzzle by the