A Multiplication Based Logic Puzzle

Today was Saint Nicholas day in much of Europe. Children woke up and looked in their shoes that they had carefully laid out the night before. They love to find their favorite candies letting them know they’ve been good this last year. In Hungary, where everyone’s behavior is considered to be a mixture of both good and bad, children also found some virgács in their shoes, letting them know they were also naughty some of the time. Today’s puzzle looks a little like virgács.

Print the puzzles or type the solution in this excel file: 12 factors 978-985

1⁴ + 2⁴ + 3⁴ + 4⁴ + 5⁴ = 979

979 is the sum of the eleven prime numbers from 67 to 109.

979 is a palindrome in base 10 and in two other bases:
454 in BASE 15
3D3 in BASE 16 (D is 13 base 10)

979 is the hypotenuse of a Pythagorean triple:
429-880-979 which is 11 times (39-80-89)

  • 979 is a composite number.
  • Prime factorization: 979 = 11 × 89
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 979 has exactly 4 factors.
  • Factors of 979: 1, 11, 89, 979
  • Factor pairs: 979 = 1 × 979 or 11 × 89
  • 979 has no square factors that allow its square root to be simplified. √979 ≈ 31.288976

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