Sinister Sudoku (2 page)

All of a sudden, Liza found herself glad that Kevin was around.

Fat Frankie wasn’t in the joint for murder, though. He was serving the tail end of a two-year stretch for criminal conspiracy. The last member of the class was the veteran convict. Chris Dalen had spent more than a decade as a guest of the state. He had a lean, compact physique, a dancer’s build—or a cat burglar’s. That fit in with Dalen’s claim to fame, breaking into a small museum to steal a pricey painting. Although it had been created almost ninety years ago by Piet Mondrian, the canvas rated as a master-piece of modern art and was worth several million dollars. Dalen’s refusal to reveal the location of the stolen artwork had kept him in a cell five times longer than Basso.

The years showed as Dalen stepped into the sunlight from the window. His skin had grown slack, the muscles stringy. The gray hair wasn’t a surprise, but the matching complexion was. That wasn’t just prison pallor, though. Dalen had suffered two heart attacks in the last six months. Liz wasn’t sure whether that came from prison food or years of stress catching up with him. His condition had won him a release, though Liza had to wonder how much time the art thief had left to enjoy his freedom.

“So this is the big day, isn’t it Chris?” she asked.

“Ze guards haff gotten ze orders,” he said in a parody of a World War II bad-guy’s accent. “After this class, we do der paperwork, und then I blow zis pop stand.”

“Well, congratulations, Herr Dalen.” Liza looked around as her students settled themselves into their seats. “Thank you all for taking part in these pilot sessions.” Ritz responded with her patented giggle, Conn looked almost bashful, Fat Frankie gave a quick nod, and Chris Dalen gave her a grin that momentarily lit up his fine features.

“I’m really interested in seeing how you handled your last assignment,” Liza went on.

Over the last ten days, they had talked a lot about sudoku puzzles. The basics seemed simple enough. Take a nine-by-nine grid and fill in the one possible solution based on the twenty-something number of clues given. All you have to do is use each of the numbers one through nine to fill in the nine spaces in each of the nine rows and columns. The grid is also broken into nine three-by-three subgrids whose nine spaces also must contain the magic digits one through nine.

Although sudoku depends on numbers, the puzzles require no arithmetical expertise—no addition, subtraction, or square roots needed. The solution depends on logic— eliminating possibilities for a given space and discovering the one and only possible inhabitant.

That wasn’t to say that sudoku were easy. Consider a chessboard, an eight-by-eight grid with thirty-two squares occupied—and the multiplicity of permutations that can be worked across it.

Achieving a sudoku solution didn’t require movement. Instead, a solver used a series of techniques that rose in complexity. In her newspaper column and in this class, Liza concentrated on what she called the twelve steps to sudoku perfection. Actually, there were only eleven techniques—the last involved peeking in the back of the book or magazine for the printed solution.

Some of the techniques were simple enough that even Ritz had mastered them. Others required time and practice—creating an educated eye to recognize certain sudoku situations. Still others played with probabilities in a way that came perilously close to the great sudoku taboo— guessing an answer.

And there were even more esoteric techniques out there, Liza knew. These were based on the kinds of complicated equations that most people encountered only on the blackboards in the background of that TV show where the math genius helped the FBI.

In her final assignment for the class, Liza had turned the tables. Instead of looking for a solution, the students had gotten the job of creating a problem. Liza gave them the world’s most basic sudoku solution, a pretty obvious setup:

The class members also received a brief set of instructions and the challenge of figuring out how to remove answers from matching spaces to create a thirty-clue sudoku.

“Who’d like to start?” she asked.

That cut off the giggling from Ritz. Her elaborate attempts to avoid meeting Liza’s eyes came straight out of junior high. Liza wanted to laugh, until she realized that Conn Lezat was doing the same thing.

Liza sighed. “I realize there was a good chance some of you couldn’t see this project all the way through.”

“Oh, that’s all right, then.” Ritz Tarleton’s voice had regained that giggly tone.

“How far did you get?” Liza asked.

“Not very,” Ritz admitted. “It was really hard!” She handed Liza an obviously incomplete grid. Liza felt her brows coming together as she looked it over.

“You filled all the spaces in the upper left and lower right boxes in numerical order. That used up more than half of your available clues—no wonder you had such a tough time trying to lay out the rest of the puzzle.” Liza reached for her copy of the instruction packet that had accompanied the grids.

“There’s no rule against it,” Ritz piped up.

“Maybe not, but why would you do that?” Kevin had to ask.

As Ritz looked at him, her foxy face went from vacuous to predatory—the cunning little vixen scooping out a plump fowl. “I have a rep to maintain, for being . . . cutting edge.”

Ritz licked her lips.

Liza did her best to keep her face calm, even as her hand clenched into fists. No doubt the warden and the prison administration would get annoyed if she smacked one of their charges. She decided to change the subject by turning to another class member. “How about you, Conn?”

Lezat had donned a pair of wire-frame eyeglasses, which he now pushed up on the abbreviated bridge of his nose. “I started out, then I came across a reference to this technique called Bowman’s Bingo.” He brought out a little envelope and poured out a little pile of those clear plastic disks some people used to mark bingo cards. Liza wondered how in hell Lezat had gotten his hands on those.

“This is a semi-recursive elimination technique that can be employed manually,” the business whiz began. “I’ve got nine sets of these chips, each marked one through nine. Now, by picking a starting point, I put a possible number facedown . . .”

As he droned on, Liza shook her head. According to the online sudoku discussion sites, Bowman’s Bingo embodied the logic both in the Forcing Chains and Nishio techniques. Some members even suggested that being able to do such a technique by hand spelled the end of sudoku solving.

She interrupted before Conn got into full lecture mode. “I’m aware of how it works,” Liza said. “I’m also aware that this is an extremely advanced solving technique, while you were supposed to be creating a simple puzzle. How far did you get?”

“Well, ah . . .” Conn finally handed over a couple of pages of cryptic calculations and a grid with only three spaces filled in. Liza had to wonder if this was why Lezat’s company had gone belly-up. Had he distracted himself with fancy ideas, plans, and strategies when he should have been taking care of business?

She turned to Fat Frankie, who gave her an almost genuine smile. The expression stayed on his face as he turned to his more hapless classmates—except he didn’t bother to hide the contempt in his eyes. “It took a while, but I think I got this to work. I had a couple of guys check it out, and they all got the same answers.”

He gave her five copies of the puzzle, plus a solution sheet.

Liza nodded, glancing over the puzzle. One thing she’d discovered—when Fat Frankie put his mind to something, he did a workmanlike job.

“That leaves you, Chris,” Liza said, turning to her final student—her best, she also suspected. Chris Dalen didn’t show it much, but he had a playful streak and a mind as agile as his body once had been. He handed her a sheet, and Liza felt a stab of disappointment. It looked as if he’d managed to put down even fewer clues than Ritz.

Dalen grinned at her expression—and passed over four more copies and the solution. “Zey tell us zat less is more,” he said. “Und zo I got by witout all zat many clues.” Liza did a quick count. Then she went back and did a slower one.

“There are only seventeen clues here.” She didn’t even attempt to keep the amazement out of her voice. “That’s the lowest number of clues that anyone has used to make a valid puzzle so far.”

“How did you—” Liza began.

Chris Dalen simply waggled his eyebrows, replying, “Ve haff vays . . .”

Holding this gem of a puzzle, Liza felt mightily tempted to grab a pencil and begin checking it out. A glance over at Frankie Basso knocked that idea out of her head, however. Fat Frankie looked definitely put out over being upstaged, and it probably wasn’t a good idea to tick off a Mafia Don, or shot-caller, or whatever organized crime rank that Basso held.

Liza frowned. If she as a civilian felt that, surely Chris, with his years in the joint, knew that fact far better.
Maybe it’s because he’s getting out today,
she thought. Then she thought,
Maybe it’s a good thing he’s getting out when he is.

That wasn’t the reason why she used Basso’s sudoku for the class discussion, though. The assignment she had given was creating a puzzle with thirty clues—and Fat Frankie was the only class member who’d done that. The thunder-clouds gradually left the mobster’s face as he started talking about his trials and triumphs constructing the sudoku.

“You said that as I took numbers away from the grid you gave me, I had to balance them out—”

“Mirror them,” Liza said.

“Yeah, mirror. So I figured the easiest way was to make the bottom half of the puzzle match the top. That made it easy enough—pick out a number up top, then go for its reverse down below.” He shook his head, frowning. “But then going back to figure out the whole puzzle again, that was a pain in the ass. Especially since that most basic sudoku you gave us made it so easy to cheat.”

“I found that, too,” Conn Lezat put in. “That’s why I thought that maybe some sort of randomizing system . . .”

Liza let him drone on for a little more, thinking,
Sure, right, take a simple job and make it ridiculously more difficult.

On the other hand, this was her first shot at teaching a class. If the students felt that the grid she’d handed out didn’t work, Liza should at least consider what they had to say.

“Okay,” she said, “I’ll work up a less distracting grid in the future.”

“That will keep the rechecking a bit more interesting,” Chris Dalen said dropping his phony accent. “I bet this would have been a lot easier with one of those computer programs that keeps a running list of all the possible candidates for each space. Me, I wouldn’t know.” The art thief shrugged. “They won’t let me anywhere near one.”

“I thought they had computers here,” Liza said.

“But not everyone has access,” Fat Frankie explained. “F’rinstance, they think I might communicate with various associates.” His smile was bland, as if that never happened.