# 1197 Mystery Level

The first few moves needed to solve this puzzle might not be too hard, but soon enough it might get a bit tougher. Nevertheless, its one solution can be found using logic and an ordinary 12×12 multiplication table. Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Here are facts about the number 1197:

• 1197 is a composite number.
• Prime factorization: 1197 = 3 × 3 × 7 × 19, which can be written 1197 = 3² × 7 × 19
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1197 has exactly 12 factors.
• Factors of 1197: 1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197
• Factor pairs: 1197 = 1 × 1197, 3 × 399, 7 × 171, 9 × 133, 19 × 63, or 21 × 57
• Taking the factor pair with the largest square number factor, we get √1197 = (√9)(√133) = 3√133 ≈ 34.59769 1197 is the sum of these eleven consecutive prime numbers:
83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 = 1197

1197 looks interesting to me when it is written in some other bases:
It’s 3330 in BASE 7 because 3(7³ + 7² + 7¹) = 3(399) = 1197,
and it’s 2255 in BASE 8.
It’s 999 in BASE 11, because 9(11² + 11 + 1) = 9(133) = 1197,
and it’s 1K1 in BASE 26 (K is 20 base 10)

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