Part 18 (1/2)

”Are they the same?”

”No,” the boy said, ”I got the other wrong somewhere.”

”S'posin' you had him right,” the puzzle-maker said, ”it took you hour.

Ordinary figures you did him in thirty-two seconds.”

”I see,” said Eric, ”it's another case of wonderful but not wonderful enough, isn't it?”

”Exactly. Here,” the other continued, reaching down a ma.n.u.script portfolio, ”is every kind of numbers ever made. You find that the Hindu--or wrongly called Arabic--numerals are the only ones wonderful enough for modern uses.”

Thoroughly interested, the boy sat down with this big ma.n.u.script book.

Weird schemes of numeration rioted over the pages, from the Zuni finger and the Chinese knuckle systems to the latest groups of symbols, used in modern higher mathematics, of which the boy had not even heard. It was noon before he realized with a start that the morning was gone.

”Oh, Dan!” he said reproachfully, ”we haven't done anything to-day.”

”Never mind,” said the old man, ”we get a start after a while.”

That afternoon, when the boy settled down to do some work on his own account, he felt a much greater friendliness to the mere look of figures. They seemed like old friends. Before, a figure had only been something in a ”sum,” but now he felt that each one had a long history of its own. Little did he realize that the biggest step of his mathematics was accomplished. Never again would he be able to look at a page of figures with revulsion. They had come to life for him.

The next morning, Eric found the old puzzle-maker busy with a chess-board.

”Aren't we going to do any work to-day, either?” he asked, disappointedly.

”Soon as I finish,” the old man answered. ”Get pencil and paper. As I move knight from square to square, you draw.”

Shrugging his shoulders slightly, but not so noticeably that the puzzle-maker could see, Eric obeyed. It seemed very silly to him. But as the knight went from square to square in the peculiar move which belongs to that piece in chess, the boy was amazed to find a wonderful and fascinating geometrical design growing under his hand.

”Another way, too,” said the old man thoughtfully, the instant the figure was finished, not giving the boy a chance to make any comment.

And, without further preface he started again. This time an even stranger but equally perfect design was formed.

”But that's great!” said Eric, ”how do you know it's going to come out like that! I wonder if I could do it?”

”Try him,” the puzzle-maker answered, getting up from the board. For half an hour Eric moved the knight about, but never got as perfect an example as the old man.

”Are there only those two ways?” said the boy at last.

”Over thirty-one million ways of moving the knight so that he occupies each square once,” was the reply. ”Every one makes a different design.”

”I'll try some this evening,” said the boy. ”But it's funny, too. Why does it always make a regular design?”

”You want to know? Very well.” And the puzzle-maker quietly explained some of the most famous mathematical problems of all time, working them out with the chessmen and the board.

”You know what they call him, magic?” queried the old man.

”Magic! No!” exclaimed Eric p.r.i.c.king 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?”