"Magic! No!" exclaimed Eric pricking up his ears at the word. "Tell me about it, Dan."
"Numbers all friends, live together, work together," the puzzle-maker answered. "I show you." And, taking pencil and paper, he dotted down in forms of squares and cubes rows and rows of figures. "Add him up," he said, "up and down, cross-wise, any way. He all make same number."
"They do, sure enough," said Eric, after testing half a dozen magic squares, "but how do you do it? Do you have to remember all those figures and just where they go?"
"Don't remember any of him," the other answered. "He has to go so."
"But I can't make them come that way," exclaimed the boy, after trying for a few minutes. "What's the trick?"
"All friends," repeated the old man, and in his curiously jolting speech he told Eric the startling links that are found in the powers of numbers. As soon as he had the principle clearly in mind, the boy found that there was no great difficulty in making up the most astonishing magic squares.
As the winter drew on, and calls for help on the stormy waters increased, the opportunities for sessions with the shrewd old mathematician grew fewer, but Eric stuck fast to his promise to spend all the time he could afford with his instructor. He was keenly disappointed that the puzzle-maker showed such an absolute disregard of the actual things the boy wanted to prepare for in his examinations. But Eric had been rigidly trained by his father in the sportsmanlike attitude of never complaining about any arrangement he had made himself, and he paid for his coaching out of his small earnings without a word. In order to make up for what he inwardly felt was lost time, he worked by himself at his books in such few minutes as he was able to snatch from his life-saving duties. And, although he was tired almost to exhaustion, many and many a day, he found that even in that work he was getting along quite well.
Eric could never get his eccentric teacher to look at the books required in his preparatory work. What was more, he had a feeling that he couldn't really be getting much good from his hours spent with Dan, because he enjoyed them so much. Early schooldays had made him associate progress with discomfort.
For example, one day Dan showed him tricks with cards—and then explained the mathematics of it, making the most puzzling mysteries seem only unusual applications of very simple principles. Another day, the puzzle-maker told him of curious problems of chance, by dice, by lotteries, and so forth, and almost before Eric realized what the old man was driving at, the essential ideas of insurance and actuary work were firmly fixed in his mind.
It was not until a couple of weeks before the expected close of navigation that the puzzle-maker said,