1690 Today Is My 8th Blogiversary!

Today’s Puzzle:

I made this Crazy-8 puzzle to commemorate the 8th anniversary of my blog.

Write the numbers from 1 to 10 in both the first column and the top row so that those numbers and the given clues work together like a multiplication table. Some of it might be a little tricky, so make sure you use logic on every step!

My eighth year of blogging has been amazing for me:

  1. Denise Gaskins has a Kickstarter going for her latest book, 312 Things to Do with a Math Journal. One of those 312 things will be journaling about some of my puzzles.
  2. I’ve also hosted her fabulous Math Education Blog Carnival and been featured when other bloggers hosted it.
  3. Bill Davidson interviewed me for his podcast, Centering the Pendulum. Although I’m not one of the many “Eureka Math Giants” he knows, my interview was included in the mix.

  4. In the spring, THREE different types of puzzles I’ve made were published in the Austin Chronicle.

  5. Also a BIG thank you to YOU, reading this right now. I really appreciate you and others who have taken the time to read my thoughts and solve my puzzles.

It’s been a wonderful year. NONE of those things would have happened if I didn’t write a blog. I feel quite fortunate and humbled by it all. I think I’ll go on for another eight years!

Factors of 1690:

  • 1690 is a composite number.
  • Prime factorization: 1690 = 2 × 5 × 13 × 13, which can be written 1690 = 2 × 5 × 13².
  • 1690 has at least one exponent greater than 1 in its prime factorization so √1690 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1690 = (√169)(√10) = 13√10.
  • The exponents in the prime factorization are 1, 1, and 2. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(2 + 1) = 2 × 2 × 3 = 12. Therefore 1690 has exactly 12 factors.
  • The factors of 1690 are outlined with their factor pair partners in the graphic below.

More About the Number 1690:

1690 is the sum of two squares in THREE different ways:
41² + 3² = 1690,
39² + 13² = 1690, and
31² + 27² = 1690.

1690 is the hypotenuse of SEVEN Pythagorean triples:
232 1674 1690, calculated from 31² – 27², 2(31)(27), 31² + 27²,
246 1672 1690, calculated from 2(41)(3), 41² – 3², 41² + 3²,
416 1638 1690, which is 26 times (16-63-65),
650 1560 1690, which is (5-12-13) times 130.
858 1456 1690, which is 26 times (33-56-65),
1014 1352 1690, calculated from 2(39)(13), 39² – 13², 39² + 13², but it is also (3-4-5) times 338, and
1190 1200 1690, which is 10 times (119-120-169).

2 thoughts on “1690 Today Is My 8th Blogiversary!

    • Thank you! You’ve been very supportive pretty much from the beginning. Thank you for that as well!

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