“I can arrange that,” Sugimoto said.
“What?”
“If you want to talk to the head of the Sekiguchi-gummi, I can arrange it. We did a show about them a year ago because they sponsored a contest to encourage sumi-e, Japanese traditional ink painting.”
“Organized crime sponsored a painting contest?”
“Junichi Sekiguchi considers himself a patron of the arts. In Japan, organized crime functions much more openly than in the United States. They still get involved in bad things, but they also have legitimate businesses they can use for things like sponsoring a contest. I’m pretty sure I can get you in to see him if you really want to talk to him. Do you want to do it today?”
“No, tomorrow. I want to make some arrangements first. Right now, I’d like to talk to Kiyohara-san.”
Within an hour I was facing Mr. Kiyohara across a metal table in a cramped conference room in the Nissan building. Excited, I launched into my solution to the problem of the blades.
“We use brute force.”
Kiyohara-san was puzzled by my statement, so I continued. “When you come right down to it, the solution is pretty simple. We’ve got six sword blades we’re dealing with and I think they fit together to form a map. The question is how do they fit together? This question is made harder by the fact that one of the blades is missing. I’ve been trying to come up with some elegant way of deducing how the blades fit together and what the map looks like, but actually this isn’t necessary.
“Although the problem looks impossibly hard, when you start moving the swords around to find all the patterns, you discover there are just twelve possibilities. That’s all. Are you familiar with the Japanese children’s game with the different shaped pieces of plastic? The one where kids move the pieces around until they make recognizable shapes?”
Puzzled, Kiyohara said, “Yes.”
“By computer we’re going to do something similar with the patterns on the blades. I’ll explain the details, but the important thing to keep in mind is that there are twelve, and only twelve, ways the blades can fit together, even when you account for the blade we don’t know about.”
“Now I’m confused,” Kiyohara said. “How can there only be twelve possibilities?”
I picked up a pencil and a sheet of paper. “Watch. From the numbers on the tangs we know where three blades fit. These are blades one, three and six. That’s Sonoda-san’s blade, the blade from Rotterdam, and my blade. We know the patterns on two of the other blades, and of course one blade is missing. Let’s call the missing blade X, and the two patterns we do have A and B. The problem is how to fit them together so we can match this pattern to a map of Japan.”
“Let’s assume that the missing blade is the second blade. Let’s label the New York blade A and assume it’s the fourth blade. The Tokyo blade, which we’ll label B, then becomes the fifth one. This is the pattern we would have.”
On the sheet of paper I wrote, “1 X 3 A B 6.”
“Now that may or may not be the real pattern formed on the blades. For instance, perhaps we have the New York blade and the Tokyo blade switched around. That would give us this pattern.”
I labeled a column two and I wrote, “1 X 3 B A 6.”
“Those are the only two variations if the missing blade is the second blade. But what if the missing blade isn’t the second blade? What if it’s the fourth blade? Well, we end up with two more patterns.”
I quickly drew the patterns on the paper. “And if the missing blade is the fifth blade we end up with this pattern.” I drew the remaining two patterns. I pointed down to the sheet of paper with the six patterns.
See, there are only six possibilities here. If we reverse the order so the numbers on the tangs go from six to one, instead of one to six, that doubles the combinations. That’s still only twelve patterns, regardless of which blade is missing and what order the Tokyo blade and the New York blade fit into the pattern. We don’t have to know which is the right pattern. All we have to do is enter all twelve into a computer program that will try to match each pattern to the Nissan digitized map of Japan.
“I know a digitized map is kept as a series of numbers, very much like the numbers you showed me for the photo enhancement. For instance, a section of a digitized map might look like this.” I took a piece of paper and a pencil and wrote:
0444444444
4044466664
4044666666
4404666666
4404444444
Kiyohara stayed silent, but as soon as I put down my pencil he said, “What’s that?”
“It’s a simplified drawing of a digitized map. For instance, zero could be water, so the string of zeros on the left side of the diagram could be a river. The number 4 could be flat farmland, and 6 could be foothills. If we knew the patterns on the six blades we could create a similar map looking at temples, rivers, and mountains. The temples and villages shown on the blades may have moved or disappeared, but it’s not likely that something like a mountain will vanish, so we’re bound to have landmarks that will line up. By computer we can match the blades’ map to the Nissan Japan map.
“After four hundred years, we’re not going to get a perfect match, but we can calculate how close a match we get and review those portions of Japan which give us as close a fit as possible. We can actually eliminate a lot of geography. We’re probably looking at a very small portion of the main island of Honshu, probably centered around Osaka castle and the surrounding countryside. Osaka was the stronghold of the Toyotomi, wasn’t it?”
Kiyohara nodded.
“If we had the pattern on the blades,” I continued, “the actual matching of the blades to your map would be easy. Our problem is we don’t have all the blades and we also don’t know how they fit together. The solution to those problems is that we don’t have to come up with an answer.”
“What?”
“Because one-sixth of the map is missing, theoretically the best match we could come up with is five-sixths, or eighty-three percent. If we had the landmarks on all six blades I suppose we could match things one hundred percent, but I’m betting that starting with an eighty-three percent match will be good enough. We can’t match perfectly, but we can narrow down the search, and maybe there are other clues that can help us.”
“How will we know the scale to use with the map on the blades?”
“We’ve got several mountains shown on the blades. If we get a match on mountain locations, we just adjust the scale to match the distance between the mountains on the digitized map. Then we look to see if things like rivers, temples, and villages align.”
“I see,” Kiyohara said. “So there are only twelve possible patterns.”
“That’s right.”
“And instead of trying to figure out which is the right pattern, we’ll just try to match all patterns, using mountains as landmarks to set the proper scale.”
“That’s right. That’s the beauty of it. By using the computer, we can try all combinations. That would be difficult to do manually, but the computer will grind away trying every combination of blade pattern to every geographic location to see if it gets a match. We can even measure how close each pattern fits. We can come up with something like a percentage scale that will measure how close each of the patterns fits to the current geography of the area. It will chew up a lot of Nissan’s computer power, but by switching things around and trying different combinations we might come up with the answer.”
Kiyohara tapped the diagram with the various combinations. “This is pretty good. You just swapped things around, trying different combinations. How did you come up with it?”