Edward sighed. “I’ve studied in many fields through the course of my life, but math was never my strong point!”
“Come on Edward, we can beat this.” Billie continued to read the puzzle left by the Atlanteans. In front of her, a single balancing scale stood threateningly at the edge of the room. Four heavy iron weights stood at its base.
“Using only these four weights — 2, 6, 18, and 27 stadia respectively, the challenger must determine how many gold ingots to place on the opposite side of the scales to achieve precisely 10 stadia.”
“Damn it! I said I didn’t like math!” Edward then studied it carefully.
Billie began scribbling the numbers and potential solutions on her tablet.
Edward was the first to see the answer. “I’ve got it!”
“What’s the answer?” Billie asked in surprise.
“It’s easy,” Edward said. “We need to place the 6-stadia weight and the 2-stadia weight on the opposite side to the 18-stadia weight and then add the gold ingots until the two sides balance. When the two groups weigh the same, then the weight of the gold ingots is equal to 10 stadia!”
Billie nodded her head.
The math appeared quite simple — too simple! She grabbed her tablet and quickly began searching for something. The slightest of crests formed on her forehead, the only sign of her stress. Quickly, she scrolled through and read the information she was after. Something was wrong, but she needed proof.
Edward started to optimistically load the scales until he balanced the same amount of gold ingots on the same side as the one with 8 stadia worth of weight. Once the scales were balanced, he took the gold ingots and said to Billie, “I guess that’s how much 10 stadia is. About twenty-five pounds!”
He was ready to place it inside the brass cup that formed the pedestal, when Billie stopped him.
“Wait!” she said.
“What is it?”
“I think we just got the entire equation wrong! I think we just overcomplicated a very simple math problem.”
“What do you mean? The math was simple. I’m sure we covered it in grade school or something. We placed the 18- stadia object on one side of the scales, followed by a 6-stadia and 2-stadia weight on the other side and then increased the weight with gold ingots until the scales balanced — leaving precisely 10 stadia worth of gold ingots! Now I’m going to take those 10 stadia worth of gold ingots and release our bridge.”
“That would be correct,” Billie said, with a tone of reassurance that clearly said that it wasn’t. “That is to say, if we were using the correct type of math, as we use today. But what if the Atlanteans used something different?”
“What do you mean? Math is the one universal constant, the language that defies borders!”
“The answers may be the same, but the method of reaching those answers vary greatly throughout history and society.”
“You’re losing me, Dr. Swan. In plain English, what have I missed?”
“We work on base ten! What’s to say that the people of Atlantis worked on the same system as we do?”
Edward looked hurt. “What’s to say that they didn’t?”
She shoved her tablet into his hands and said, “This!”
His eyes scrolled over the page, while his eyes stared in blank confusion. Math, she realized, really wasn’t his forte.
“According to this, the early inhabitants of the Congo Basin used duodecimal systems, as well as the most ancient tribal communities in the Himalayan Mountains of Nepal.” Billie held her notepad in her hand and then looked up and said, “Who else do we know lived in both those places?”
“The survivors of Atlantis!”
“Exactly. Why else would they evolve to use such a unique base system?”
“Christ! The people of Atlantis worked in base twelve!”
Billie nodded her head. “Therefore, we need to calculate this using base twelve.”
“Base twelve?” Edward looked confused having just agreed with her argument. “Just because my grandfather stole most of the orichalcum left in Atlantis doesn’t mean I actually know much about the place. What do you mean by base twelve?”
Billie began explaining it to him in simple terms. “Mathematics is standard. The universal language. It doesn’t matter where you come from — math is math.”
“Right,” he agreed.
“Only that assumption’s wrong. We work on base ten. Most likely because that’s how many fingers we have. Meaning we count to ten, then hundreds, which are just tens of tens, followed by thousands which is tens of hundreds, and so on.”
“All right. Now I’m following you. I’m sure we learned about this stuff somewhere. The ancient Atlanteans didn’t use this method?”
“No. They worked out of base twelve. That means they counted to twelve and then moved to sets of twelve, followed by sets of sets of twelve.”
“Okay, so now what have we got?” Edward said, frustrated.
“Using this unique system…” Billie thought about it and then scribbled on her tablet several times until she reached an answer. “The numbers 2, 6, 18, and 26 in the game now become — 2, 6, 20, and 30 in base 10. The number 18 actually means 12 plus 8, which we all know equals 20 in base 10. And the number, 26 actually means, 2 x 12 plus 6, which equals 30.”
“Okay, that makes sense,” Edward said, although it didn’t. “So that being the case, we can work out how many gold ingots equal 20 stadia and then halve it to reach the goal of 10 stadia worth of gold?” Edward suggested.
“No, because we’re no longer looking for 10 stadia in weight.”
“But the puzzle said…”
“10 in base 12 is 12!”
Realization struck Edward!
“Which means the problem becomes very simple — we take 18 on one side and place the 2 and the 6 weight on the other to make 10, which is really 12 stadia!”
“Exactly!”
Billie and Edward carefully balanced the scale until they were confident they had reached 12 stadia of gold.
Edward looked at her and said, “You’re certain this will work, Dr. Swan?”
Beneath a smile filled with sweat, Billie replied, “Certain enough that I’m willing to bet my life on it!”
“That’s good enough for me.”
Edward, keen to discover the truth, then carefully placed the gold ingots on the pedestal.
Nothing happened.
Then the ground began to shake with the force of an earthquake. Above them, stone rubble fell from a ceiling that had lost its strength. The two quickly retreated toward the entrance of the room, which was covered by stone arches.
Chapter Fifty-Three
By the time the rubble had subsided, the chasm was replaced by a single bridge of fallen stone no more than a few feet wide, but easily able to be traversed. Billie looked at the almost perfectly formed passage.
“It looks stable enough. What do you think?” she asked.
“I still think you’re a genius, Dr. Swan!” He grabbed one of her hands and squeezed it with the warm affection of an old man. “Thank you.”
Carefully, they crossed the chasm and after crawling through a narrow tunnel, reached the third challenge. Again, it appeared to be a relatively large cavern, but this time the entire room was separated by 20 tall stones, which reached up toward them, like totem poles. From their height, Billie and Edward could step along most of them and reach the other side, but any misjudgment of their footing and they would fall to their deaths.
The steps ranged from one to three feet apart and at points were narrow enough that whoever was attempting to cross would have only enough room to place one foot on it. Even so, with only mild circumspection, even an 80-year-old man could make his way across to the level ground on the other side.