How easy or difficult is this mystery level puzzle? That’s part of the mystery! Once you solve it, you will know, and you don’t have to tell let anybody else know.

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

• 1209 is a composite number.
• Prime factorization: 1209 = 3 × 13 × 31
• 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 1209 has exactly 8 factors.
• Factors of 1209: 1, 3, 13, 31, 39, 93, 403, 1209
• Factor pairs: 1209 = 1 × 1209, 3 × 403, 13 × 93, or 31 × 39
• 1209 has no square factors that allow its square root to be simplified. √1209 ≈ 34.7707

Did you notice the pattern in the factors?  3×13×31 = 1209
39 and 93 are two of its factors, as well!

1209 is also the hypotenuse of a Pythagorean triple:
465-1116-1209 which is (5-12-13) times 93

The factors in the multiplication table puzzle below are not in the usual order. Can you figure out where each factor from 1 to 10 belongs in both the first column and the top row?

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

Here are a few facts about the number 1208:

• 1208 is a composite number.
• Prime factorization: 1208 = 2 × 2 × 2 × 151, which can be written 1208 = 2³ × 151
• The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 × 2 = 8. Therefore 1208 has exactly 8 factors.
• Factors of 1208: 1, 2, 4, 8, 151, 302, 604, 1208
• Factor pairs: 1208 = 1 × 1208, 2 × 604, 4 × 302, or 8 × 151
• Taking the factor pair with the largest square number factor, we get √1208 = (√4)(√302) = 2√302 ≈ 34.75629

1208 is also the sum of consecutive prime numbers:
601 + 607 = 1208

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)

Today I’m saying “Happy Birthday” to my son, Brent with a yummy but mysterious puzzle cake. I’ve made the puzzle just a little bit harder than normal.

Adding 13 to the puzzle actually makes it easier to solve, but adding 14 makes some multiples of 7 more difficult. For example, the allowable common factors of 70 and 35 are now 7 AND 5, and the allowable common factors of 28 and 56 are now 4, 7, and 14.

As always there is only one solution. I know my son can solve this puzzle, Can you?

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Now I’ll share some facts about the number 1191:

• 1191 is a composite number.
• Prime factorization: 1191 = 3 × 397
• 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 1191 has exactly 4 factors.
• Factors of 1191: 1, 3, 397, 1191
• Factor pairs: 1191 = 1 × 1191 or 3 × 397
• 1191 has no square factors that allow its square root to be simplified. √1191 ≈ 34.51087

1191 is the hypotenuse of a Pythagorean triple:
684-975-1191 which is 3 times (228-325-397)

1191 is repdigit 111 in BASE 34 because
34² + 34 + 1 = 35(34) + 1 = 1191

The difficulty level of a Mystery Level puzzle is somewhere between fairly easy to extra hard. You won’t know how easy or how difficult it is until you give it a try. Use logic, not guessing and checking, and have fun with it!

Print the puzzles or type the solution in this excel file: 10-factors-1174-1186

What can I tell you about the number 1185?

• 1185 is a composite number.
• Prime factorization: 1185 = 3 × 5 × 79
• 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 1185 has exactly 8 factors.
• Factors of 1185: 1, 3, 5, 15, 79, 237, 395, 1185
• Factor pairs: 1185 = 1 × 1185, 3 × 395, 5 × 237, or 15 × 79
• 1185 has no square factors that allow its square root to be simplified. √1185 ≈ 34.42383

1185 is the hypotenuse of a Pythagorean triple:
711-948-1185 which is (3-4-5) times 237

I think 1185 looks interesting when it is written in some other bases:
It’s palindrome 102201 in BASE 4,
357 in BASE 19, and
palindrome 151 in BASE 32

The sets of clues in this Mystery Level puzzle have more than one possible common factor. Don’t guess which one you should use. In each case, the right factor can be selected by using logic. Will you figure out where all the factors from 1 to 10 go?

Print the puzzles or type the solution in this excel file: 10-factors-1174-1186

Here are a few facts about the number 1184:

• 1184 is a composite number.
• Prime factorization: 1184 = 2 × 2 × 2 × 2 × 2 × 37, which can be written 1184 = 2⁵ × 37
• The exponents in the prime factorization are 5 and 1. Adding one to each and multiplying we get (5 + 1)(1 + 1) = 6 × 2 = 12. Therefore 1184 has exactly 12 factors.
• Factors of 1184: 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, 1184
• Factor pairs: 1184 = 1 × 1184, 2 × 592, 4 × 296, 8 × 148, 16 × 74, or 32 × 37
• Taking the factor pair with the largest square number factor, we get √1184 = (√16)(√74) = 4√74 ≈ 34.4093

1184 is the hypotenuse of a Pythagorean triple:
384-1120-1184 which is 32 times (12-35-37)

1184 looks interesting to me in a few other bases:
It’s 5252 in BASE 6,
3311 in BASE 7,
987 in BASE 11,
828 in BASE 12, and
WW in BASE 36 (W is 32 base 10)
That one is because 32(36) + 32(1) = 32(37) = 1184

There are thirteen clues in this Mystery Level Find the Factors 1 – 12 puzzle. Will those thirteen clues bring you good luck or bad? The logic needed to solve the puzzle may be a bit complicated, but if you stick with it, you will figure it out. Good luck to you!

Print the puzzles or type the solution in this excel file: 12 factors 1161-1173

Let me share some facts about the number 1172:

• 1172 is a composite number.
• Prime factorization: 1172 = 2 × 2 × 293, which can be written 1172 = 2² × 293
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1172 has exactly 6 factors.
• Factors of 1172: 1, 2, 4, 293, 586, 1172
• Factor pairs: 1172 = 1 × 1172, 2 × 586, or 4 × 293
• Taking the factor pair with the largest square number factor, we get √1172 = (√4)(√293) = 2√293 ≈ 34.23449

1172 is the sum of six consecutive prime numbers:
181 + 191 + 193 + 197 + 199 + 211 = 1172

34² + 4² = 1172

1172 is the hypotenuse of a Pythagorean triple:
272-1140-1172 calculated from 2(34)(4), 34² – 4², 34² + 4²
It is also 4 times (68-285-293)

1172 is a palindrome in a couple of bases:
It’s 818 in BASE 12 because 8(12²) + 1(12) + 8(1) = 1172,
and 494 in BASE 16 4(16²) + 9(16) + 4(1) = 1172

This mysterious multiplication table does not have its factors in the usual places. Can you use logic to figure out where the factors from 1 to 10 go so that the given clues belong where they are?

Print the puzzles or type the solution in this excel file: 10-factors-1148-1160

What can I tell you about the number 1159?

• 1159 is a composite number.
• Prime factorization: 1159 = 19 × 61
• 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 1159 has exactly 4 factors.
• Factors of 1159: 1, 19, 61, 1159
• Factor pairs: 1159 = 1 × 1159 or 19 × 61
• 1159 has no square factors that allow its square root to be simplified. √1159 ≈ 34.04409

1159 is the sum of the twenty-five prime numbers from 3 to 101.

1159 is the hypotenuse of a Pythagorean triple:
209-1140-1159 which is 19 times (11-60-61)

The twelve clues in this puzzle are easy to see, but solving the mystery of the puzzle might not be so easy. The clues work together to point to particular factors. Can you figure out where they all go?

Print the puzzles or type the solution in this excel file: 10-factors-1148-1160

Now I’ll write a little bit about the number 1158:

• 1158 is a composite number.
• Prime factorization: 1158 = 2 × 3 × 193
• 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 1158 has exactly 8 factors.
• Factors of 1158: 1, 2, 3, 6, 193, 386, 579, 1158
• Factor pairs: 1158 = 1 × 1158, 2 × 579, 3 × 386, or 6 × 193
• 1158 has no square factors that allow its square root to be simplified. √1158 ≈ 34.0294

1158 is the hypotenuse of a Pythagorean triple:
570-1008-1158 which is 6 times (95-168-193)

1158 is 123 in BASE 33 because 33² + 2(33) + 3(1) = 1158