Reflections on the Third Week of Fall - Puzzled

    Three Thursdays ago, a smiling curly headed fifth grader at Learning Center asked, “Would you like to try our math puzzle, Janet?”

    “Yes,” I said. “I like puzzles.”

    The youngster and two of his friends had created a number table containing six rows of five boxes. Each box had an addition, subtraction, multiplication, or division sign and a number. Holding the paper in his left hand he said, “Start at one of the three arrows on top.” He waved his thin, right pinkie finger horizontally then vertically. “Move this way or that–no diagonals. Exit with fifty. That means you'll be at forty-five when you get to the plus five box at the bottom.”

    I took the paper. “Thanks. I'll work on it at home.” How hard could it be? To solve the puzzle I just had to calculate along a path.

    Three different afternoons I made trial and error runs through the maze, doodled numbers on scratch paper, and decided to ask for more clues when I volunteered again. Two Thursdays ago, I checked with the curly haired youngster to see if the path could go up as well as down.

    He held his chin with his hand for a moment then said, “I guess so, but you can't go through any square twice.”

    I also asked the teacher, “Are negative numbers or fractions involved?”

    She shook her head. “But you go over fifty. It took me an hour and a half to solve Sunday night.”

    I'd already spent more time than that. Maybe I needed help. Spence doesn't like puzzles or games so I wouldn't ask him. His high school friend Eric and Eric's wife Kay would be arriving the next day. Eric, a retired electrical engineer, was a whiz at math. Kay had trained teachers and liked games. I could ask them–after they'd had time to settle in.

    Friday afternoon, Kay and I prepared home grown vegetables–honey boat squash, purple beans, and zucchini. Spence cooked pork and chicken. After a leisurely dinner, we watched jazz videos on the large flat screen TV. The puzzle could wait.

    Saturday I baked a pie with Wells Wood apples and blueberries. Kay cooked swiss steak with Wells Wood tomatoes. We played Banana Grams and Dutch Blitz. The fellas took a walk in the dark and drizzle. At bed time I casually mentioned, “I got a math puzzle from the children at the school where I volunteer. Maybe you could help me solve it?”

    Kay shrugged.

    Eric chuckled. “Sure.”

    Sunday after breakfast, I pushed away the breakfast dishes and placed the puzzle on the kitchen table between Kay and me. She studied the puzzle. “You have to do this by trial and error,” she said. “There are millions of combinations.”

    “The students probably wrote their sequence of numbers then just filled in the spaces around them,” I said.

    We worked top down, bottom up, and top down again. Six scribbled pages of figures later, we still didn't have the solution.

    “Eric,” Kay called. “Will you help us?”

    He chuckled, put down his electronic book, and stared at the puzzle.

    Kay and I roasted two home grown pie pumpkins and made pumpkin soup for lunch.

    Eric calculated, drew circles connected by arrows, and wrote numbers. After forty-seven scattered circles, he didn't have the solution either.

    We put the puzzle aside, ate the soup, and packed for a late afternoon/evening Erie outing. We walked through a tunnel of trees on the Sidewalk Trail from the Presque Isle Lighthouse to Misery Bay then drove under a rainbow to the Bayfront Grille for a gourmet dinner. On the way home, Kay told us about playing in a Dixieland jazz band at Geauga Lake amusement park, and we listened to The Bad Plus on a CD.

    This past Monday, the day Eric and Kay would leave, I was desperate. When Eric took his second sip of coffee, I shoved the puzzle at him. He chuckled. We munched breakfast and figured. “We've got to try every possible path,” I said. I drew a copy of the puzzle and jumped up to fetch my colored pencils.

    “That's a dead end,” Eric said when a path proved false.

We'd try another direction. Six colors later on three marked charts, we had tried every whole number combination from top to bottom and bottom to top. None worked.

   “We must have made an calculating error,” I said and chose the path that started plus eleven, minus one, divided by five. Lucky guess. We'd made an error on the tenth step in the sequence. That path worked.

    Kay walked into the kitchen, yawned, and held out her hand for the paper. She studied our numbers. “You made a mistake . . . no that's right.” She handed the paper back. “Fun.”

  This past Thursday, I took the completed puzzle to the curly haired fifth grader. “I finished,” I said and handed it to him.

    He grinned and pumped his fist.