### Blog Submission Appeal:

Please, tell me how you’ve made K-12 math education more fun. You see, later this month I’m hosting the Playful Math Education Blog Carnival. I have found several great blog posts to share, but maybe I haven’t seen yours. You can share your blog post with me by submitting this official form, leaving a comment below, or messaging me on twitter, Iva Sallay@findthefactors.com. I look forward to reading your post! Please share it with me by Saturday, August 22 so it can be included in this month’s carnival.

### Today’s Puzzle:

This mystery-level puzzle was modeled after a carnival ride, the swing carousel, a ride that tilts slightly as it goes around, and lets you ride by the seat of your pants. My puzzle might not be the best representation of that ride, but it hopefully got your attention.

Embellishing the puzzle might make it more eye-catching, but it is probably easier to solve the puzzle without distracting color and lines. (It’s a mystery-level puzzle, so I’m keeping how easy or difficult it is a secret.) Here is a plain version of the same puzzle:

### Factors of 1508:

- 1508 is a composite number.
- Prime factorization: 1508 = 2 × 2 × 13 × 29, which can be written 1508 = 2² × 13 × 29.
- 1508 has at least one exponent greater than 1 in its prime factorization so √1508 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1508 = (√4)(√377) = 2√377.
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1508 has exactly 12 factors.
- The factors of 1508 are outlined with their factor pair partners in the graphic below.

### More about the Number 1508:

1508 is the sum of two squares in two different ways:

32² + 22² = 1508

38² + 8² = 1508

1508 is the hypotenuse of FOUR Pythagorean triples:

540-1408-1508, calculated from 32² – 22², 2(32)(22), 32² + 22²,

580-1392-1508, which is (5-12-**13**) times **116,**

608-1380-1508, calculated from 2(38)(8), 38² – 8², 38² + 8²,

1040-1092-1508 which is (20-21-**29**) times **52.**