1206 and Level 6

If you carefully study all the clues in this Level 6 puzzle and use logic, you should be able to solve the puzzle. Stick with it and you’ll succeed!

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Here are some facts about the number 1206:

  • 1206 is a composite number.
  • Prime factorization: 1206 = 2 × 3 × 3 × 67, which can be written 1206 = 2 × 3² × 67
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1206 has exactly 12 factors.
  • Factors of 1206: 1, 2, 3, 6, 9, 18, 67, 134, 201, 402, 603, 1206
  • Factor pairs: 1206 = 1 × 1206, 2 × 603, 3 × 402, 6 × 201, 9 × 134, or 18 × 67,
  • Taking the factor pair with the largest square number factor, we get √1206 = (√9)(√134) = 3√134 ≈ 34.72751

Notice that 6·201 = 1206. Not very many numbers can equal themselves by using their own digits in a different way with +, -, ×, ÷, and/or parenthesis. That fact makes 1206 only the seventeenth Friedman Number.

1206 is also the sum of the twenty prime numbers from 19 to 103.

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