e in the eight
directions as before."

"Here you are!" cried Grigsby, after he had been scribbling for a few
minutes on the back of an envelope.

The Professor smiled indulgently.

"Are you sure that there is a current English postage-stamp of the value
of threepence-halfpenny?"

"For the life of me, I don't know. Isn't there?"

"That's just like the Professor," put in Hawkhurst. "There never was such
a 'tricky' man. You never know when you have got to the bottom of his
puzzles. Just when you make sure you have found a solution, he trips you
up over some little point you never thought of."

"When you have done that," said the Professor, "here is a much better one
for you. Stick English postage stamps so that every three divisions in a
line shall add up alike, using as many stamps as you choose, so long as
they are all of different values. It is a hard nut."

[Illustration]

69.--_The Frogs and Tumblers._

"What do you think of these?"

The Professor brought from his capacious pockets a number of frogs,
snails, lizards, and other creatures of Japanese manufacture--very
grotesque in form and brilliant in colour. While we were looking at them
he asked the waiter to place sixty-four tumblers on the club table. When
these had been brought and arranged in the form of a square, as shown in
the illustration, he placed eight of the little green frogs on the
glasses as shown.

"Now," he said, "you see these tumblers form eight horizontal and eight
vertical lines, and if you look at them diagonally (both ways) there are
twenty-six other lines. If you run your eye along all these forty-two
lines, you will find no two frogs are anywhere in a line.

"The puzzle is this. Three of the frogs are supposed to jump from their
present position to three vacant glasses, so that in their new relative
positions still no two frogs shall be in a line. What are the jumps
made?"

"I suppose----" began Hawkhurst.

"I know what you are going to ask," anticipated the Professor. "No; the
frogs do not exchange positions, but each of the three jumps to a glass
that was not previously occupied."

"But surely there must be scores of solutions?" I said.

"I shall be very glad if you can find them," replied the Professor with a
dry smile. "I only know of one--or rather two, counting a reversal, which
occurs in consequence of the position being symmetrical."

70.--_Romeo and Juliet._

For some time we tried to make these li