Over the Humbug’s strenuous objections, Milo and Tock decided to swim, and, protesting loudly, the bug was dragged along with them toward the sea.

Canby hurried off to answer more questions, and the last thing he was heard to say was “Pardon me, can you tell me who I am?”

They swam and swam and swam for what seemed like hours, and only Tock’s firm encouragement kept Milo struggling through the icy water. At last they reached the shore, thoroughly exhausted and, except for the bug, completely soaked.

“That wasn’t bad at all,” the Humbug said, straightening his tie and brushing himself off. “I must visit there again.”

“I’m sure you will,” gasped Milo. “But from now on I’m going to have a very good reason before I make up my mind about anything. You can lose too much time jumping to Conclusions.”

The car was just where they’d left it, and in a moment they were on their way again as the road turned away from the sea and began its long climb into the mountains. The warm sun and billowy breezes dried them as they went.

“I hope we reach Digitopolis soon,” said Milo, thinking of the breakfast they hadn’t eaten. “I wonder how far it is.”

Up ahead, the road divided into three and, as if in reply to Milo’s question, an enormous road sign, pointing in all three directions, stated clearly:

“Let’s travel by miles,” advised the Humbug; “it’s shorter.”

“Let’s travel by half inches,” suggested Milo; “it’s quicker.”

“But which road should we take?” asked Tock. “It must make a difference.”

As they argued, a most peculiar little figure stepped nimbly from behind the sign and approached them, talking all the while. “Yes, indeed; indeed it does; certainly; my, yes; it does make a difference; undoubtedly.”

He was constructed (for that’s really the only way to describe him) of a large assortment of lines and angles connected together into one solid many-sided shape—somewhat like a cube that’s had all its corners cut off and then had all its corners cut off again. Each of the edges was neatly labeled with a small letter, and each of the angles with a large one. He wore a handsome beret on top, and peering intently from one of his several surfaces was a very serious face. Perhaps if you look at the picture you’ll know what I mean.

When he reached the car, the figure doffed his cap and recited in a loud clear voice:

“My angles are many.

My sides are not few.

I’m the Dodecahedron.

Who are you?”

“What’s a Dodecahedron?” inquired Milo, who was barely able to pronounce the strange word.

“See for yourself,” he said, turning around slowly. “A Dodecahedron is a mathematical shape with twelve faces.”

Just as he said it, eleven other faces appeared, one on each surface, and each one wore a different expression.

“I usually use one at a time,” he confided, as all but the smiling one disappeared again. “It saves wear and tear. What are you called?”

“Milo,” said Milo.

“That is an odd name,” he said, changing his smiling face for a frowning one. “And you only have one face.”

“Is that bad?” asked Milo, making sure it was still there.

“You’ll soon wear it out using it for everything,” replied the Dodecahedron. “Now I have one for smiling, one for laughing, one for crying, one for frowning, one for thinking, one for pouting, and six more besides. Is everyone with one face called a Milo?”

“Oh no,” Milo replied; “some are called Henry or George or Robert or John or lots of other things.”

“How terribly confusing,” he cried. “Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You’d have to say Robert plus John equals four, and if the four’s name were Albert, things would be hopeless.”

“I never thought of it that way,” Milo admitted.

“Then I suggest you begin at once,” admonished the Dodecahedron from his admonishing face, “for here in Digitopolis everything is quite precise.”

“Then perhaps you can help us decide which road to take,” said Milo.

“By all means,” he replied happily. “There’s nothing to it. If a small car carrying three people at thirty miles an hour for ten minutes along a road five miles long at 11:35 in the morning starts at the same time as three people who have been traveling in a little automobile at twenty miles an hour for fifteen minutes on another road exactly twice as long as one half the distance of the other, while a dog, a bug, and a boy travel an equal distance in the same time or the same distance in an equal time along a third road in mid-October, then which one arrives first and which is the best way to go?”

“Seventeen!” shouted the Humbug, scribbling furiously on a piece of paper.

“Well, I’m not sure, but——” Milo stammered after several minutes of frantic figuring.

“You’ll have to do better than that,” scolded the Dodecahedron, “or you’ll never know how far you’ve gone or whether or not you’ve ever gotten there.”

“I’m not very good at problems,” admitted Milo.

“What a shame,” sighed the Dodecahedron. “They’re so very useful. Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve feet high and six feet wide in two days, all you would need to build Boulder Dam is a beaver sixty-eight feet long with a fifty-one-foot tail?”

“Where would you find a beaver that big?” grumbled the Humbug as his pencil point snapped.

“I’m sure I don’t know,” he replied, “but if you did, you’d certainly know what to do with him.”

“That’s absurd,” objected Milo, whose head was spinning from all the numbers and questions.

“That may be true,” he acknowledged, “but it’s completely accurate, and as long as the answer is right, who cares if the question is wrong? If you want sense, you’ll have to make it yourself.”

“All three roads arrive at the same place at the same time,” interrupted Tock, who had patiently been doing the first problem.

“Correct!” shouted the Dodecahedron. “And I’ll take you there myself. Now you can see how important problems are. If you hadn’t done this one properly, you might have gone the wrong way.”

“I can’t see where I made my mistake,” said the Humbug, frantically rechecking his figures.

“But if all the roads arrive at the same place at the same time, then aren’t they all the right way?” asked Milo.

“Certainly not!” he shouted, glaring from his most upset face. “They’re all the wrongway. Just because you have a choice, it doesn’t mean that any of them hasto be right.”

He walked to the sign and quickly spun it around three times. As he did, the three roads vanished and a new one suddenly appeared, heading in the direction that the sign now pointed.

“Is every road five miles from Digitopolis?” asked Milo.

“I’m afraid it has to be,” the Dodecahedron replied, leaping onto the back of the car. “It’s the only sign we’ve got.”

The new road was quite bumpy and full of stones, and each time they hit one, the Dodecahedron bounced into the air and landed on one of his faces, with a sulk or a smile or a laugh or a frown, depending upon which one it was.

“We’ll soon be there,” he announced happily, after one of his short flights. “Welcome to the land of numbers.”

“It doesn’t look very inviting,” the bug remarked, for, as they climbed higher and higher, not a tree or a blade of grass could be seen anywhere. Only the rocks remained.