Games & Puzzles Magazine - Theseus and the Minotaur

This is adapted from the article on the Theseus maze that appeared in the April 1994 issue of the British magazine Games & Puzzles

## Theseus and the Minotaur

### by Robert Abbott

Theseus Popalopos lived a quiet life as a computer programmer in California’s Silicon Valley. Every now and then a colleague at work would ask about his unusual name and he’d have to explain about his father, Aegeus Popalopos, owner of the Athenian Diner in New York City. Aegeus was very proud of his Greek heritage and he named his son Theseus because he was convinced the son was the direct descendant (after 132 generations) of King Theseus, the ruler of Athens.

Theseus Popalopos knew the myths that surrounded King Theseus: how the Cretan King Minos created the labyrinth to hold the Minotaur, how he forced the Athenians to send youths to be sacrificed to the Minotaur, and how Theseus was to be sacrificed but instead killed the Minotaur and found his way out of the labyrinth. Popalopos thought these stories were interesting, but he felt they had nothing to do with him and the thought his father could be pretty boring when the subject of heritage came up. He later learned—to his horror—that there was someone who was very serious about this heritage, more serious than his father had ever been. |  |

One Friday evening, as he returned from the weekly beer bash given by his company, he was set upon by five men who wrestled him to the ground, drugged him, and carried him off. He awoke three days later on a small tropical island in the Pacific. He was told that next month he would be sacrificed during the Great Festival.

One of the natives who had brought him there explained that the island was inhabited by a tribe that practiced human sacrifice. It was part of their heritage but was rare in this modern age. (This had been explained to the native by Joseph Campbell, who had visited the island thirty years ago.) Theseus noticed that his fear was beginning to be replaced by boredom as he heard more talk about heritage. But he became very interested when the native told him how the sacrifice took place: the victim was placed in a labyrinth where he was eaten by a creature they called the Minotaur. And Theseus was more amazed when he learned that the ruler of the island was not a native but someone from a different island, the island of Crete. And this ruler called himself King Minos the 132nd.

Theseus spent the next day exploring. The natives allowed him to walk freely since they knew there was no way he could escape. Theseus found the island to be rather pleasant, though he felt he would have enjoyed it a lot more if the natives hadn’t planned to make a human sacrifice out of him.

As he walked along a beach he came upon the most beautiful woman he had ever seen. She smiled at him and said, “You are Theseus. I know all about you. I am Ariadne, daughter of King Minos.”

Theseus felt a sudden bond with this woman, and he thought that here at last was someone who might make some sense. He pleaded with her to tell him who King Minos the 132nd was and why he planned to feed him to the Minotaur.

“You must try to understand my father,” she said. “He used to be one of the richest men in the world and owned a large shipping company headquartered in Crete. His company was destroyed by the corrupt government in Athens and he lost most of his money. He became depressed, retreated into drink and drugs, and worst of all, he spent all his time doing nothing but solving mazes that he found in various books. This last activity finally caused his mind to snap.

“He decided that Crete had suffered too long under Athens. In his maddened state, he felt that the way to make Crete preeminent again was to build a labyrinth and then revive the ancient ceremony where Athenian youths were sacrificed to the Minotaur. Father then declared himself to be King Minos the 132nd. He is from a Cretan family so he might well be a descendant of the ancient King Minos. At the same time he changed my name to Ariadne—it used to be Debbie. I’m only half Cretan; my mother was an American.”

Ariadne (or Debbie) paused in her long narrative. Theseus urged her to continue—to explain how they ended up on this Pacific island.

“Father soon realized that it would be politically difficult to revive human sacrifice on Crete. While reading one of Joseph Campbell’s books, he learned about the natives on this island who practiced a rite that was surprisingly similar to the ancient Cretan rite. He took all the money he had left and he and I came to the island. Father became a great benefactor to the islanders and they were happy to make him their king. They also had no objection when he made a small modification to their sacrificial ceremony: the addition of a minotaur.”

“Okay, wait a minute,” said Theseus. “So far this almost makes sense. But where did your father find a minotaur?”

“Well,” replied Ariadne, “actually the Minotaur is just a robot.”

“A robot! I expected at least some sort of half-man, half-bull horrible kind of monster.”

“That’s exactly what my father wanted, and he went so far as to contract with Genes R Us, the San Jose, California, firm that specializes in recombinant DNA. They tried some gene-splicing experiments but couldn’t come up with anything that resembled a minotaur. Their research had one amusing outcome, though. An anti-genetic research group got wind of what was happening, and they went on all the television talk shows to declare that Genes R Us was creating a half-man, half-bull monster that would lay waste the countryside. For once, what they said was absolutely true, but it was so preposterous that no one believed them. The group lost all credibility, and now genetic research proceeds without fear of protest.

“Father decided that if he couldn’t have a biological minotaur, he’d have to settle for a robot; so he hired Daedalus Incorporated, an artificial intelligence firm in San Jose, to create him one. It’s very effective. It doesn’t actually eat you, but if it catches you it will destroy you.”

“And I guess that’s the end of the story.”

“Well, not quite,” said Theseus. How did your father learn about me?”

“Oh, yes. He was flying to Athens where he planned to kidnap some Athenian youths to be the first victims in his labyrinth. He made a stopover in New York and had breakfast at the Athenian Diner. He heard the old Greek who owned the diner telling another patron that his son was a descendant of King Theseus. Father thought that a descendant of King Theseus would make a much better victim than just anyone from Athens; so he sent five of the natives to capture you, and here you are.”

Theseus and Ariadne talked on into the night, and soon they were declaring their love for each other. Ariadne said she would try to help Theseus escape from the labyrinth.

Ariadne met Theseus the next day and gave him a map she had drawn of the labyrinth. “I’m surprised the labyrinth is so simple,” Theseus said. “It would be easy for anyone to find the way out.”

“Yes,” she said, “it would be very simple if it didn’t have a minotaur in it. You are placed in the maze at the spot I’ve marked with a T. The Minotaur starts at the spot marked M. Unlike the ancient myth, you don’t have to kill the Minotaur. All you have to do is leave by the exit at the upper right. Once you’re outside the walls of the labyrinth, the Minotaur won’t follow you.”

“Okay,” said Theseus, “it looks like I might have a chance. Tell me what you know about the Minotaur.”

“The Minotaur has sensors that tell it which of its four sides is next to a wall. Also, there are sensors placed throughout the labyrinth that radio information to the Minotaur about your location. Thus the Minotaur always knows where you are. And finally, the Minotaur can move twice as fast as you.”

“Oh no,” Theseus said, “if the Minotaur knows where I am and it’s twice as fast as me, how could I possible escape it?”

“I don’t know,” said Ariadne. “This is beginning to look hopeless.”

They both sat for a long time staring at the map of the maze, trying to think of a way to get past the Minotaur. Finally Theseus had an idea. “I just realised,” he said, “that there’s one thing we don’t know: we don’t know how the Minotaur thinks.”

“What do you mean?”

“Well, the Minotaur may know where I am, but finding something in a maze involves a lot of decisions. If we knew how the Minotaur makes its decisions, how it chooses which corridor to travel down, then maybe we can figure out a way to outsmart it.”

“So, how can we learn about the Minotaur’s decision-making processes?”

“If I had a listing of the computer program that controls the Minotaur, I might be able to work it out.”

“I’ll see what I can do.”

That night Ariadne broke into King Minos’ office and found a listing of the program. She brought it to Theseus the next day. He was happy to see that it was in a computer language he understood. He went off by himself and spent three days studying the program. When he returned he told Ariadne that he now knew how the Minotaur made its decisions, and he was ready to explain it to her.

“Okay,” said Ariadne, “but try to keep the explanation simple because I know very little about computers.”

“Actually it’s not that complicated,” said Theseus, “because, fortunately for us, the Minotaur is pretty stupid.”

“First of all, it will be easier if we think of this as a game between me and the Minotaur. I’ll divide the map into squares, like squares on a game board.” Theseus drew light lines on the map and it now looked like the diagram above.

“First I take a turn, and I can move one square. Then, since the Minotaur can move twice as fast as me, he takes two turns. To determine how the Minotaur moves on each of his turns, simply follow the instructions on this sheet.” Theseus handed her a write-up he had made titled ‘Program for One Move by the Minotaur.’ It’s an overall summary of part of the computer program that controls the Minotaur.

PROGRAM FOR ONE MOVE BY THE MINOTAUR

1. Can the Minotaur move horizontally and get closer to Theseus? If Yes, go to Paragraph 2. If No, go to Paragraph 3.
2. Move Horizontally one square towards Theseus. Then go to paragraph 5.
3. Can the Minotaur move vertically and get closer to Theseus? If Yes, go to Paragraph 4. If No, go to Paragraph 5.
4. Move vertically one square towards Theseus. Then go to paragraph 5.
5. End of turn.

“So far, so confusing,” said Ariadne.

“I realize that,” said Theseus, “but here are some sample moves that will explain everything.” He handed her yet another piece of paper which contained the diagram shown below.

“Suppose Theseus is at the position labeled T1 (let’s refer to me in the third person here) and the Minotaur is at M1. It’s Theseus’ turn and he decides to move south one square to T2. Now it’s the Minotaur’s turn. If we go twice through the Minotaur’s program, we see that it would move to M2. If Theseus then goes to T3, the Minotaur would move to M3; and if Theseus goes to T4, the Minotaur would move to M4. The Minotaur is now on the same square as Theseus and would have captured him.”

“I see,” said Ariadne. “So, even though the program for the Minotaur is simple, it can be effective. I don’t understand, though, why you say the Minotaur is stupid.”

“Well,” said Theseus, “for one thing it can’t think ahead. Also its program has a minor flaw that I might be able to exploit: the program asks the question about horizontal movement before it asks the question about vertical movement. That causes the program to choose a horizontal move whenever possible, even in cases where a vertical move would be a lot smarter.

“Let me give another example. Suppose Theseus is at T5 and the Minotaur is at M5. If Theseus moves to T6, the Minotaur would move to M6. Now suppose Theseus moves to T7. To us humans it would appear that the best move for the Minotaur would be to move south then east to capture Theseus. But the Minotaur doesn’t think that way. If you strictly follow the program for the Minotaur, you’ll find that he would move to M7. Theseus could continue to T8 and the Minotaur would move to M8; then Theseus could move to T9 and the Minotaur to M9. Finally Theseus could move to T10 and the Minotaur would make no move. Theseus could then continue out of the labyrinth.”

“You’re right,” said Ariadne, “the Minotaur does appear to act rather stupidly. It should be easy for us to figure out a path you can take through the labyrinth that will keep the Minotaur from capturing you.”

“Okay,” said Theseus. “Let’s each of us work on this problem and we can meet tomorrow to compare our solutions.”

They met the next day and were surprised to find that neither of them was able to work out a solution, and they were becoming anxious because the Great Festival was to take place in only two weeks. They both worked frantically on the maze and finally, on the night before the festival, Ariadne discovered the solution. She drew a route on the diagram and gave it to Theseus.

On the day of the festival, Theseus was placed in the labyrinth. He followed the route Ariadne had drawn for him and he was able to walk out of the labyrinth. King Minos declared that Theseus could go free, and Theseus and Ariadne left for Hawaii, where they planned to marry.

So, what is the route that Theseus can take to get out of the labyrinth? A few loose ends need to be cleared up: Theseus makes the first move and he must exit the labyrinth. He can’t stay hidden behind a wall, for eventually he would starve to death. However, on any turn Theseus can choose not to move. In some rare instances it can be to his advantage to let the Minotaur take extra turns.

Probably the best way to work on the maze is to place one pencil on Theseus’ starting point and a second pencil on the Minotaur’s starting point. Take a turn for Theseus, moving one (or zero) squares. Then take two turns for the Minotaur by going twice through the Minotaur’s program. This will result in the Minotaur moving zero, one or two squares. After you get used to the way the Minotaur moves you’ll probably want to skip reading through the program. That’s okay, but be sure not to move the Minotaur vertically when it’s possible for him to move horizontally.

There’s basically only one solution to the maze (which took me 4 hours to find!—Ed), but at some points there are alternate routes that Theseus could take. The solution involves between ninety and a hundred moves on the part of Theseus.

This story is an expanded version of a story from Robert Abbott’s book Mad Mazes, published by Bob Adams Inc, 260 Center Street, Holbrook, MA 02343, USA.

To Games & Puzzles' solution to the maze

For a darker view of the mythical hero Theseus, see my essay on sacred labyrinths

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