A Multiplication Based Logic Puzzle

A problem is a chance for you to do your best

A few weeks ago Brilliant Quotes tweeted a quote from Duke Ellington: “A problem is a chance for you to do your best.”

I immediately thought of problems students are given in mathematics classes because this quote applies to those problems.

It also applies to any other kind of problem a person may face. Sometimes those problems are much more challenging than problems involving numbers. All problems are opportunities for us to do our best.

Let’s find the factoring information for a relatively easy number – 393.

  • 393 is a composite number.
  • Prime factorization: 393 = 3 x 131
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 393 has exactly 4 factors.
  • Factors of 393: 1, 3, 131, 393
  • Factor pairs: 393 = 1 x 393 or 3 x 131
  • 393 has no square factors that allow its square root to be simplified. √393 ≈ 19.824

Is 393 in any Pythagorean triples?

  • 393-524-655  which is [3 – 4 – 5] times 131
  • 393-25740-25743 which is [131-8580-8581] times 3
  • Primitive 393-8576-8585
  • and Primitive 393-77224-77225

At the end of his post a-promise-broken, Established1962 tells a personal and very funny story involving his copy of Duke Ellington’s autobiography, “Music Is My Mistress.” The quote above is included in that book.

 

 

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Comments on: "393 and A Chance to Solve a Problem" (2)

  1. Very motivational! Is this how you persuade your students to solve more problems?

    Liked by 1 person

  2. ivasallay said:

    Good idea! I’ve mostly thought of what this quote could do to motivate ME! Now I will have to share it with my students as well.

    Like

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