A Multiplication Based Logic Puzzle

If your shopping cart were a go-kart, you would have an advantage getting all the shopping bargains Black Friday offers. Not only would you be able to move much faster than the average shopping cart, but you would also be able to do wheelies to get through the crowds, around corners, or tight spaces. After you complete the shopping spree of your dreams, you can lie down exhausted, but ecstatic and work on a puzzle, like this one.

Print the puzzles or type the solution in this excel file: 12 factors 959-967

I realize I’m really pushing it to make this puzzle have a Thanksgiving week theme. I love that Black Friday has turned into Black November because it means bargains without all the crowds.

You can also imagine the puzzle is a toy on a child’ wishlist. Whatever you think, I hope you enjoy solving the puzzle.

Here’s a little about prime number 967:

It is 595 in BASE 13 because 5(13²) + 9(13¹) + 5(13⁰) = 967
It is also 1J1 in BASE 23 (J is 19 in base 10) because 1(23²) + 19(23¹) + 1(23⁰) = 967

  • 967 is a prime number.
  • Prime factorization: 967 is prime.
  • The exponent of prime number 967 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 967 has exactly 2 factors.
  • Factors of 967: 1, 967
  • Factor pairs: 967 = 1 × 967
  • 967 has no square factors that allow its square root to be simplified. √967 ≈ 31.09662

How do we know that 967 is a prime number? If 967 were not a prime number, then it would be divisible by at least one prime number less than or equal to √967 ≈ 31.1. Since 967 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, or 31, we know that 967 is a prime number.


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