A Multiplication Based Logic Puzzle

994 and Level 1

All you need is these eleven clues and the multiplication facts in a normal 12 × 12 multiplication table to completely fill in every square of this abnormal multiplication table, I mean puzzle. Don’t worry about how fast you can solve the puzzle. The more puzzles you solve the better you will get at doing them. Relax and enjoy yourself!

Print the puzzles or type the solution in this excel file: 12 factors 993-1001

When is the number 994 a palindrome?
It is 4334 in BASE 6 because 4(6³) + 3(6²) + 3(6¹) + 4(6⁰) = 994, and
it’s 464 in BASE 15 because 4(15²) + 6(15¹) + 4(15⁰) = 994

  • 994 is a composite number.
  • Prime factorization: 994 = 2 × 7 × 71
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 994 has exactly 8 factors.
  • Factors of 994: 1, 2, 7, 14, 71, 142, 497, 994
  • Factor pairs: 994 = 1 × 994, 2 × 497, 7 × 142, or 14 × 71
  • 994 has no square factors that allow its square root to be simplified. √994 ≈ 31.52777

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