Before computers were machines, computers were people who computed things. This complicated task often fell to women because it was considered basically clerical. That’s right: computing triple integrals all day long qualified as clerical.
Two of the most popular New Year’s Resolutions are to spend more time with family and friends, and to get more exercise. The 2017 Mathematics Game is a prime opportunity to do both at once.
So grab a partner, slip into your workout clothes, and pump up those mental muscles!
For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.
Use the digits in the year 2017 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
You must use all four digits. You may not use any other numbers.
Solutions that keep the year digits in 2-0-1-7 order are preferred, but not required.
You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.
My Special Variations on the Rules
You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
You MAY use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. I’m including these because Math Forum allows them, but I personally try to avoid the beasts. I feel much more creative when I can wrangle a solution without invoking them.
The carnival features prime numbers, self-referential logic, calculus puns, word problems, Pythagorean triples, arithmetic games, geometric coloring designs, and more.
Counting all the fractional variations, my massive blog post 30+ Things to Do with a Hundred Chart now offers nearly forty ideas for playing around with numbers from preschool to prealgebra.
If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.
Since I’ve been posting new Alexandria Jones stories this week (beginning here), I’ve gone back and re-read the old Christmas posts. I noticed that the original Graph-It Game included a religious design, but nothing for those who don’t celebrate Christmas.
So I updated the post with a new, non-religious puzzle. Here it is, if you want to play…
Graph-It Game Design
For this design, you will need graph paper with coordinates from −8 to +8 on both the x- and y-axis. Connect the points in each line. Stop at the periods, and then start a new line at the next point.
For toddler Renée’s Christmas gift, Alex and Leon crafted a puzzle set of wooden blocks.
First, they made a sturdy box with circle, square, and triangle shapes cut in the lid.
To make the blocks large and baby-safe, Alex and Leon bought a 4-foot 2×2 board. Then they asked Uncle Will to help them create a set of special blocks to fit through the holes.
Each block was round and square and triangular, so it could fit exactly through any of the three holes.
She drew the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs would bend easily.
She cut out shapes until her fingers felt bruised: 20 each of the pentagon and hexagon, 40 each of the triangle and square.
Alex bought a bag of small rubber bands for holding the tabs together. Each rubber band can hold two tabs, forming an edge of the polyhedron. So, for instance, it takes six squares and twelve rubber bands to make a cube.
Finally, she stuffed the whole kit in a plastic zipper bag, along with the following instructions.
Polyhedra Have “Many Faces”
Poly means many, and hedron means face, so a polyhedron is a 3-D shape with many faces.
The plural of polyhedron is polyhedra, thanks to the ancient Greeks, who didn’t know that the proper way to make a plural was to use the letter s.
Each corner of a polyhedron is called a vertex, and to make it more confusing, the plural of vertex is vertices.
Regular Polyhedra
Regular polyhedra have exactly the same faces and corners all around. If one side is a square, then all the sides will be squares. And if three squares meet to make one vertex, then all the other vertices will be made of three squares, just like that first one.
There are only five possible regular polyhedra. Can you figure out why?
Here are the five regular polyhedra, also called the Platonic solids. Try to build each of them with your construction kit.
Tetrahedron: three equilateral triangles meeting at each vertex.
Hexahedron: three squares meeting at each vertex. Do you know its common name?
Octahedron: four triangles at each vertex.
Icosahedron: five triangles at each vertex.
Dodecahedron: three pentagons per vertex.
You can find pictures of these online, but it’s more challenging to build them without peeking at the finished product. Just repeat the vertex pattern at every corner until the polygons connect together to make a complete 3-D shape.
Semi-Regular Polyhedra
Semi-regular polyhedra have each face a regular polygon, although not all the same. Each corner is still the same all around. These are often called the Archimedean polyhedra.
For example, on the cuboctahedron, every vertex consists of a square-triangle-square-triangle combination.
Here are a few semi-regular polyhedra you might try to build, described by the faces in the order they meet at each corner:
Here’s how Alex created tetra-tetraflexagon Christmas cards to send to her friends:
1. Buy a pack of heavy paper at the office supply store. Regular construction paper tears too easily.
2. Measure and divide the paper into fourths one direction and thirds the other way. Fold each line backward and forward a few times.
3. Number the front and back of the paper in pencil, lightly, as shown. Then carefully cut a center flap along the dotted lines.
4. Fold the paper along the dark lines as shown, so the center flap sticks out from underneath and the right-hand column shows all 2’s.
5. Fold the flap the rest of the way around to the front and fold the right-hand column under again. (Shown as dark lines on the diagram.) This makes the front of the flexagon show 1’s in every square.
6. Carefully, tape the flap to its neighbor on the folded column. Don’t let the tape stick to any but these two squares.
7. Gently erase your pencil marks.
Find All the Faces
A tetra-tetraflexagon has four faces: front, back, and two hidden. It is shaped like a tetragon — better known as a rectangle.
Here’s how to flex your tetra-tetraflexagon card:
Face 1 is easy to find. It’s on top when you make the card.
Turn the card over to find Face 2.
Face 3 is hidden behind Face 2. Fold your flexagon card in half (vertically) so that Face 1 disappears. Unfold Face 2 at the middle, like opening a book. Face 3 should appear like magic.
Face 4 is hidden behind Face 3. Fold the card (vertically) to hide Face 2, then open the middle of Face 3. Face 2 vanishes, and Face 4 is finally revealed.
When Faces 2 and 3 are folded to the back, you will notice that any pictures you drew on them will look scrambled. What happened?
Add Your Designs
Alex wrote a holiday greeting on Face 1. Then she drew Christmas pictures on the other three faces of her card.
The Jones family sat around the dining table performing a traditional holiday ritual: the Christmas card assembly line.
First, Dr. Fibonacci Jones (the world-famous mathematical archaeologist) signed for himself and his wife. He handed the card to Alex, who signed for herself and baby Renée. Then Alex’s younger brother Leon added his own flourish. Finally, Mrs. Jones wrote a personal note on the cards going to immediate family and close friends.
One-year-old Renée sat in her high chair, chewing the corners of an extra card.
Alex Poses a Problem
Alex dropped her pen and shook out her tired fingers.
“I’m stumped,” she said. “I’d like to send a special Christmas card to some of my friends from camp last summer. But I can’t think of anything that seems good enough.”
Leon leaned his chair back in thought.
Then he snapped his fingers. “I’ve got it! We’ll throw a handful of sand in each of their envelopes. You know, to make them remember all the fun you guys had digging up old stuff.”
Alex humphed. “How would you like to get sand in your Christmas present?” she asked. “Besides, it wasn’t stuff. It was artifacts.”
“You should not make such a display of your ignorance, young man,” Dr. Jones said. “Stuff, indeed!”
Mrs. Jones put her hand to her forehead and sighed dramatically. Then she turned to Alex. “Have you considered doing a jigsaw puzzle card? They sell them at the hobby store.”
“I’ve tried those before,” Alex said, “but the ones I had always warped. The puzzles didn’t go back together very well.”
Dad Gets an Idea
Dr. Jones got an out-of-focus, “I’m thinking” look in his eyes. He stood up, tapped his chin with his pen, and walked away. He almost ran into the wall, but he caught himself. Shaking his head, he disappeared into his study.
Mrs. Jones put down her pen and picked up Renée.
“Why don’t you two address those envelopes while we wait for your dad’s inspiration to reveal itself? I need to put a little one down to S-L-E-E-P.”
Alex laughed. “If you keep that up, Renée will learn to spell before she’s out of diapers!”
Leon thumbed the stack of envelopes and groaned. “C’mon, sis. Back to work!”
Before long, Mrs. Jones came back and chased the kids away from the table. “I’ll finish this,” she said.
Unfolding the Magic
Alex and Leon ran to the study. They found Dr. Jones at his desk, playing with a piece of paper.
“Ah, there you are,” he said. “Here, Alex. What do you think?”
“Well,” she said, “it looks like a regular piece of paper that’s been folded over on itself.”
Dr. Jones nodded. “Now you know a sheet of paper has two faces—that is, it has a front and a back.”
Leon reached for the paper and flipped it over. “Is that why you put red stripes on one side and blue stripes on the other?”
“Observe,” Dr. Jones said.
He took the piece of paper and folded it in half. Then he unfolded it and handed it to Alex.
“Hey, how’d you do that?” she asked. “Now there are blue polka-dots on this side.”
“Cool! It’s magic,” Leon said.
“It is called a tetra-tetraflexagon,” Dr. Jones said, “and it has one more hidden face. Can you find it?”
Alex folded the paper this way and that. Then she held it up in triumph.
“Look, red dots—I did it!”
She gave her dad a tremendous hug. “Thanks, Dad! I’ll make magic flexagons. They’ll be the best Christmas cards ever!”
Greetings from my Math Circle kids, and best wishes for a grace-filled holiday season.
My December “Let’s Play Math” newsletter went out yesterday to everyone who signed up for Tabletop Academy Press math updates. This month’s issue featured infinite series and Vi Hart’s Apollonian Doodle Game.
If you’re a subscriber but didn’t see your newsletter, check your Updates or Promotions tab (in Gmail) or your Spam folder.
And if you missed this month’s edition, no worries — there will be more playful math snacks coming soon. Click the link below to sign up today!
For toddler Renée’s Christmas gift, Alex and Leon crafted a puzzle set of wooden blocks. 
Here’s how Alex created tetra-tetraflexagon Christmas cards to send to her friends: 
Denise Gaskins' Let's Play Math 