1185 Mystery Level

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

Advertisements

1184 Mystery Level

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

1172 Mystery Puzzle

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

1171 The Best Team in the Best Conference

The NCAA college football season has not had a single game, yet you can find out which team is in first place through twenty-fifth place now or anytime during the season by looking here. How are these football standings determined? By FIFTEEN people voting. Sure, it’s only one of several polls, but the four teams who play for the national championship are determined by a computer that uses polls like that one. Can you believe that there are people who find that rather unsatisfying? Your team could finish the season with the exact same record as one of those four teams but not be allowed to compete for the championship.

What do college football teams have to play for then? Almost every team is in a conference. They can play hoping to win their conference. Those teams who have a winning record can also be selected to play in one of 38 bowl games in December or early January. Winning a bowl game allows a team to finish the season with a win and is an honor to the school. Other than that, 35 of those bowl games mean absolutely nothing.

Perhaps this is a bit simplistic, but why can’t each conference send their best teams to play in bowl games against teams from a different conference. The conference that wins the most bowl games would be deemed the best conference.  The team that won that conference’s championship would be the best team in the best conference and the national champion. Every bowl game would then be important. Each eligible team would still only have to play one bowl game. More people would watch EVERY bowl game which would cause them all to make more money. The sports stations would also make more money as they keep their viewers updated with the win/loss records for every conference week after week.

Of all the things that are happening in the world today, this issue is far from being the most important, but thinking about it, like sports or this football-shaped mystery level puzzle, is a nice diversion.

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

Here’s the same puzzle but without all the color.

Now I’ll write a few things about the number 1171:

  • 1171 is a prime number.
  • Prime factorization: 1171 is prime.
  • The exponent of prime number 1171 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1171 has exactly 2 factors.
  • Factors of 1171: 1, 1171
  • Factor pairs: 1171 = 1 × 1171
  • 1171 has no square factors that allow its square root to be simplified. √1171 ≈ 34.21988

How do we know that 1171 is a prime number? If 1171 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1171 ≈ 34.2. Since 1171 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1171 is a prime number.

1171 is the sum of seven consecutive prime numbers:
151 + 157 + 163 + 167 + 173 + 179 + 181 = 1171

1171 is a palindrome in three bases:
It’s 14141 in BASE 5 because 5⁴ + 4(5³) + 5² + 4(5) + 1 = 1171,
1J1 in BASE 26 (J is 19 base 10) because 26² + 19(26) + 1 = 1171,
and 191 in BASE 30 because 30² + 9(30) + 1 = 1171

1159 Mystery Level

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)

1158 Mystery Level

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

1146 Mystery Level

This puzzle might start off easy enough, but soon afterward you will have to consider some serious logic in order to complete it. Good luck!

Print the puzzles or type the solution in this excel file: 12 factors 1134-1147

Now let me tell you about the number 1146:

  • 1146 is a composite number.
  • Prime factorization: 1146 = 2 × 3 × 191
  • 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 1146 has exactly 8 factors.
  • Factors of 1146: 1, 2, 3, 6, 191, 382, 573, 1146
  • Factor pairs: 1146 = 1 × 1146, 2 × 573, 3 × 382, or 6 × 191
  • 1146 has no square factors that allow its square root to be simplified. √1146 ≈ 33.85262

1146 is a palindrome in two other bases:
It’s 14041 in BASE 5 because 1(5⁴) + 4(5³) + 0(5²) + 4(5¹) + 1(5⁰) = 1146,
and it’s 282 in BASE 22 because 2(22²) + 8(22) + 2(1) = 1146

1145 Mysterious Butterfly

This adventurous butterfly invites you to solve its mystery. Be warned, it might not be as easy as it seems. Don’t write any factors down unless you are SURE they belong where you’re putting them. Let logic be your guide.

Print the puzzles or type the solution in this excel file: 12 factors 1134-1147

Here are more facts about the number 1145:

  • 1145 is a composite number.
  • Prime factorization: 1145 = 5 × 229
  • 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 1145 has exactly 4 factors.
  • Factors of 1145: 1, 5, 229, 1145
  • Factor pairs: 1145 = 1 × 1145 or 5 × 229
  • 1145 has no square factors that allow its square root to be simplified. √1145 ≈ 33.83785

28² + 19² = 1145
32² + 11² = 1145

1145 in the hypotenuse of FOUR Pythagorean triples
300-1105-1145 which is 5 times 60-221-229
423-1064-1145 calculated from 28² – 19² , 2(28)(19) , 28² + 19²
687-916-1145 which is (3-4-5) times 229
704-903-1145 calculated from 2(32)(11) , 32² – 11² , 32² + 11²

1145 is a palindrome in two bases:
It’s 515 in BASE 15 because  5(15²) + 1(15) + 5(1) = 1145, and
1I1 in BASE 26 (I is 18 base 10) because 26² + 18(26) + 1 = 1145

1132 Mystery

There are ten simple clues in this Mystery Level puzzle. That’s all that is needed to come up with the unique solution. Can you find it?

Print the puzzles or type the solution in this excel file: 10-factors-1121-1133

Now I’ll share some facts about the number 1132:

  • 1132 is a composite number.
  • Prime factorization: 1132 = 2 × 2 × 283, which can be written 1132 = 2² × 283
  • 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 1132 has exactly 6 factors.
  • Factors of 1132: 1, 2, 4, 283, 566, 1132
  • Factor pairs: 1132 = 1 × 1132, 2 × 566, or 4 × 283
  • Taking the factor pair with the largest square number factor, we get √1132 = (√4)(√283) = 2√283 ≈ 33.64521

1132 is the sum of two consecutive prime numbers:
563 + 569 = 1132

1132 is palindrome 1A1 in BASE 29 (A is 10 base 10) because
29² + 10(29) + 1 = 1132

1131 Mystery

You can’t know if this puzzle is easy or difficult by just looking at it. Give it a try. You might be surprised by your ability to do this puzzle!

Print the puzzles or type the solution in this excel file: 10-factors-1121-1133

Here are some facts about the number 1131:

  • 1131 is a composite number.
  • Prime factorization: 1131 = 3 × 13 × 29
  • 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 1131 has exactly 8 factors.
  • Factors of 1131: 1, 3, 13, 29, 39, 87, 377, 1131
  • Factor pairs: 1131 = 1 × 1131, 3 × 377, 13 × 87, or 29 × 39
  • 1131 has no square factors that allow its square root to be simplified. √1131 ≈ 33.63034

1131 is the hypotenuse of FOUR Pythagorean triples:
405-1056-1131 which is 3 times (135-352-377)
435-1044-1131 which is (5-12-13) times 87
456-1035-1131 which is 3 times (152-345-377)
780-819-1131 which is (20-21-29) times 39

1131 looks interesting in a couple of other bases:
It’s 939 in BASE 11 because 9(11²) + 3(11) + 9(1) = 1131
234 in BASE 23 because 2(23²) + 3(23) + 4(1) = 1131