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."

"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."

Hawkhurst, curiously enough, hit on the solution at once, and the Professor remarked that this was just one of those puzzles that a person might solve at a glance or not master in six months.

See answer