Quotations

Welcome to the 170th edition of the Playful Math Education Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 170th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Puzzle: Prime Permutations

According to Tanya Khovanova’s Number Gossip, 170 is the smallest composite number where exactly four permutations of its digits make prime numbers.

To find permutations, think of all the different ways you can arrange the digits 1, 7, 0 into three-digit numbers. (When the zero comes first, those permutations actually make two-digit numbers, which DO also count.)

Can you figure out which permutations make prime numbers?

Hint: The permutation that makes the number “170” is not prime, but it is the product of three prime numbers. Which ones?

For Younger Children: The 170 Square

A Latin square is a grid filled with permutations: letters, numbers, or other symbols so that no row or column contains more than one of any character. You’ve probably seen the popular Latin-square puzzle called Sudoku. A Graeco-Latin square (also called an Euler square) is two independent Latin squares overlapping each other.

Can you complete this Euler square made by overlapping permutations of the digits of 170 with winter colors? Don’t repeat the same color OR the same number in any row or column.

Click here for all the mathy goodness!

Welcome to the 152nd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing. There’s so much playful math to enjoy!

We didn’t have a volunteer host for January, so I’m squeezing this in between other commitments. This is my third no-host-emergency carnival in the last year, which is NOT sustainable. If you’d like to help keep the Playful Math Carnival alive, we desperately need hosts for 2022!

By tradition, we start the carnival with a puzzle or activity in honor of our 152nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Math Journaling with Prime Numbers

Cool facts about 152: The eighth prime number is 19, and 8 × 19 = 152. When you square 152, you get a number that contains all the digits from 0–4. You can make 152 as the sum of eight consecutive even numbers, or as the sum of four consecutive prime numbers.

But 152 has two real claims to fame:

• It’s the smallest number that is the sum of the cubes of two distinct odd primes.
• And it’s the largest known even number you can write as the sum of two primes in exactly four ways.

So here’s your math investigation prompt:

• Play around with prime numbers. Explore their powers, their sums, and anything else about them you like.

• What do you notice? What do you wonder?

• What’s the most interesting number relationship you can find?

Continue reading Playful Math #152: Auld Lang Syne Edition