## Math Teachers at Play #85 via ZenoMath

Feature photo above by epSos .de via Flickr (CC BY 2.0).

There’s a feast of mathematical games and activities at this month’s Math Teachers at Play blog carnival Enjoy!

“Math Teachers at Play is a monthly blog carnival that compiles posts from several blogs under the theme of teaching math in unique and innovative ways. We’re thrilled to partner with them this edition and couldn’t help ourselves from including some interesting trivia and riddles centered on our edition number – Happy Number 86!

Happy Numbers are numbers whose digits are such that – when squared and added iteratively, the number 1 is reached. For example,

82 + 62 = 100
12 + 02 + 02 = 1
So 86 is a happy number!…”

## Puzzle: Crystal Ball Connection Patterns

In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.

Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.

On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.

Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.

For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system Telephone numbers.

• Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?
T(0) = ?
T(1) = ?
T(2) = ?
T(3) = ?
T(4) = 10 connection patterns (as above)
T(5) = ?
T(6) = ?
and so on.

Hint: Don’t forget to count the state of the system when no one is on the phone crystal ball.

Feature photo at top of post by Christian Schnettelker (web designer) and wizard photo by Sean McGrath via Flickr. (CC BY 2.0) This puzzle was originally featured in the Math Teachers At Play (MTaP) math education blog carnival: MTaP #76.

## New Fantasy Novel by Homeschooled Teen Author

After months of editing, formatting, proofreading, sweat, and tears:

Teresa Gaskins’s new ebook Hunted: The Riddled Stone ~ Book Two is available now at Amazon worldwide.

To celebrate the release of Hunted, the ebook version of Banished‌—‌the first book in the Riddled Stone series‌—‌will be on sale for 99 cents for the next few weeks.

Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

## Math Game: Fan Tan (Sevens)

Feature photo above by Morgan (meddygarnet) via Flicker (CC BY 2.0).

Math Concepts: sorting by attribute (card suits), counting up, counting down, standard rank of playing cards (aces low).
Players: two or more, best with four to six.
Equipment: one complete deck of cards (including face cards), or a double deck for more than six players. Provide a card holder for young children.

### How to Play

Deal out all the cards, even if some players get more than others. The player to the dealer’s left begins by playing a seven of any suit. If that player does not have a seven, then the play passes left to the first player who does.

After that, on your turn you may lay down another seven or play on the cards that are already down. If you cannot play, say, “Pass.”

Once a seven is played in any suit, the six and the eight of that suit may be played on either side of it, forming the fan. Then the five through ace can go on the six in counting-down order, and the nine through king can go on the eight, counting up. You can arrange these cards to overlap each other so the cards below are visible, or you can square up the stacks so only the top card is seen.

## Playful Math Snacks for May 2015

The May “Let’s Play Math” newsletter went out Monday morning to everyone who signed up for Tabletop Academy Press math updates.

This month’s issue focuses on math games, from Rosie’s Princess in the Dungeon to Jim Pai’s Trig & Logarithm War. What fun!

If you missed this month’s edition, no worries—‌there will be more playful math snacks next month. Click the link below to sign up now, and we’ll send you our free math and writing booklets, too!

And remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

## Math Games with Factors, Multiples, and Prime Numbers

Students can explore prime and non-prime numbers with these free favorite classroom games:

For \$15-20 you can buy a downloadable file of the beautiful, colorful, mathematical board game Prime Climb. Or pick up the full Prime Climb game box at Amazon.

Or you can try the following game by retired Canadian education professor Jerry Ameis:

### Factor Finding Game

Math Concepts: multiples, factors, composite numbers, and primes.
Players: only two.
Equipment: pair of 6-sided dice, 10 squares each of two different colors construction paper, and the game board (click the image to print it, or copy by hand).

On your turn, roll the dice and make a 2-digit number. Use one of your colored squares to mark a position on the game board. You can only mark one square per turn.

• If your 2-digit number is prime, cover a PRIME square.
• If any of the numbers showing are factors of your 2-digit number, cover one of them.
• BUT if there’s no square available that matches your number, you lose your turn.

The first player to get three squares in a row (horizontal, vertical, or diagonal) wins. Or for a harder challenge, try for four in a row.

Feature photo at top of post by Jimmie via flickr (CC BY 2.0). This game was featured in the Math Teachers At Play (MTaP) math education blog carnival: MTaP #79. Hat tip: Jimmie Lanley.