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 little reptiles perform the feat allotted to them, and failed. The Professor, however, would not give away his solution, but said he would instead introduce to us a little thing that is childishly simple when you have once seen it, but cannot be mastered by everybody at the very first attempt. "Waiter!" he called again. "Just take away these glasses, please, and bring the chessboards." "I hope to goodness," exclaimed Grigsby, "you are not going to show us some of those awful chess problems of yours. 'White to mate Black in 427 moves without moving his pieces.' 'The bishop rooks the king, and pawns his Giuoco Piano in half a jiff.'" "No, it is not chess. You see these two snails. They are Romeo and Juliet. Juliet is on her balcony, waiting the arrival of her love; but Romeo has been dining, and forgets, for the life of him, the number of her house. The squares represent sixty-four houses, and the amorous swain visits every house once and only once before reaching his beloved. Now, make him do this with the fewest possible turnings. The snail can move up, down, and across the board and through the diagonals. Mark his track with this piece of chalk." [Illustration] "Seems easy enough," said Grigsby, running the chalk along the squares. "Look! that does it." "Yes," said the Professor: "Romeo has got there, it is true, and visited every square once, and only once; but you have made him turn nineteen times, and that is not doing the trick in the fewest turns possible."