[Photo by West Point Public Affairs.]
Alexandria Jones pulled the last sheet of chocolate chip cookies from the oven and inhaled deeply. Mmm! Perfect. And just in time — Mom was calling her to the car. She slid the cookies into a plastic bowl but left the lid off so the steam could escape. The Jones family was going to meet Uncle Will and Alex’s cousin Sam for a tail-gate picnic before the big football game.
Symbolic Logic Part I was published in 1896. When Lewis Carroll (Charles Lutwidge Dodgson) died two years later, Part II was lost. Because they couldn’t find the manuscript, many people doubted that he ever wrote Part II. But almost eighty years after his death, portions of Part II were recovered and finally published. The following puzzles are from the combined volume, Lewis Carroll’s Symbolic Logic, edited by William Warren Bartley, III.
These puzzles are called soriteses or polysyllogisms. Carroll began with a series of “if this, then that” statements. He rewrote them to make them more confusing, and then he mixed up the order to create a challenging puzzle.
Given each set of premises, what conclusion can you reach?
Looking around the room, Alex saw kids and parents moving from one table to another. Everyone seemed to be enjoying the Homeschool Math Carnival. She had six junior-high and high school students at her table, waiting while she shuffled her deck of cards.
“Okay,” she said. “These are Math Cards. I took out the face cards, so we just have numbers.”
Uncle Will drove in from the tree farm to drop off Alex’s cousin, Sam, so he could go to the Homeschool Math Carnival.
“Hey, Sam,” Alex said. “What’s in the sack?”
Sam smiled. “A secret puzzle.”
“Aw, c’mon,” Leon whined. “We’ll be busy with our own games at the carnival. Can’t you show us now?”
Maria Jones hung up the phone and collapsed at the kitchen table. She buried her head in her hands and groaned. Alex looked up from her game of Solitaire.
“Let me guess,” she said. “Can’t-Say-No Syndrome, again?”
Mrs. Jones nodded. “This time I volunteered to plan an activity for next month’s homeschool group meeting.”
Leon wandered in and pulled an apple from the fruit bowl. “Ha!” he said. “She means she volunteered us to plan an activity, right?”
Mrs. Jones smiled. “That’s my motto: When in doubt, delegate!”
Continue reading Alexandria Jones and the Mathematical Carnival
Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original posts. If you’re stuck, read the hints. Then go back and try again. Figure them out for yourself — and then check the answers just to prove that you got them right.
This post offers hints and answers to puzzles from these blog posts:
[Photo by audi_insperation.]
[In The Birthday Surprise, Alex discovered her family was expecting a new member…]
What will the baby look like, Alex wondered. “Dad, is there any way to tell whether the baby will have blue eyes like I do, or brown like the rest of the family?”
Dr. Jones shuffled the papers on his desk and found a blank page. “Over 100 years ago, the Austrian monk Gregor Mendel studied genetics, or how various traits are passed down from one generation to another.” He began to draw a diagram as he talked.
[Photo by D Sharon Pruitt.]
[July 27th is Alex’s birthday, which she shares with Johann Bernoulli, an irascible mathematician from the late 17th century.]
The guests had gone. Alex and her family sat around the table, sharing the last tidbits of birthday cake and ice cream. Alex smiled at her parents.
“Thanks, Mom and Dad,” she said. “It was a great party.”
Maria Jones, Alex’s mother, leaned back in her chair. “I do have one more surprise for you, Alex. But you will have to share this one with the whole family.”
Leon groaned. “I know what it is: Let’s all pitch in to clean up.”
“That wouldn’t be a surprise,” Alex said.
[Photo by Ella’s Dad.]
Throughout history, around the world, people in every culture have enjoyed playing games of chance. Strangely, mathematicians did not begin to study chance and probability until the 17th century.
I’ve fallen behind on my project of transcribing my Alexandria Jones stories. Finally, here are a few more tidbits from math history, along with links to relevant Internet sites and a few math puzzles for your students to try.
I hope you find them interesting.
Continue reading Math History Tidbits: Agnesi, Euler, and China
Denise Gaskins' Let's Play Math 