1193 Math Carnival Games

During the last week of every month, there is a math education blog carnival happening somewhere in the blogosphere. This month it will happen on my blog! Why do I get to host it? I sent an email to Denise Gaskins who coordinates the carnival and requested the privilege. If you would like to host it in the future, let her know.

In the meantime, you can help me with my carnival. Math can be so much fun for kids from preschool age and even all the way up to high school. If you blog about how that, I would love to include one or more of your posts in my carnival. You’ve poured your heart and soul into your posts, so why not promote it at no cost to you?  Don’t be shy! I want to read it, and other people will want to read it, too.

The deadline for submitting posts to my carnival is Friday, August 24th. There is a form for you to submit a link to your post on Denise Gaskins website. Then the following week you will be able to enjoy the carnival even more because of your participation!

Now it will be my pleasure to tell you a few facts about the number 1193:

  • 1193 is a prime number.
  • Prime factorization: 1193 is prime.
  • The exponent of prime number 1193 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1193 has exactly 2 factors.
  • Factors of 1193: 1, 1193
  • Factor pairs: 1193 = 1 × 1193
  • 1193 has no square factors that allow its square root to be simplified. √1193 ≈ 34.53983

How do we know that 1193 is a prime number? If 1193 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1193 ≈ 34.5. Since 1193 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1193 is a prime number.

1193 is the sum of five consecutive prime numbers:
229 + 233 + 239 + 241 + 251 = 1193

32² + 13² = 1193

1193 is the hypotenuse of a Pythagorean triple:
832-855-1193 calculated from 2(32)(13), 32² – 13², 32² + 13²

Here’s another way we know that 1193 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 32² + 13² = 1193 with 32 and 13 having no common prime factors, 1193 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1193 ≈ 34.5. Since 1193 is not divisible by 5, 13, 17, or 29, we know that 1193 is a prime number.

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1187 and Level 1

What is the biggest number that can divide all the clues in today’s puzzle without leaving a remainder? If you can answer that question, then you also know the greatest common factor of all those clues. It really is that simple. You can solve this puzzle!

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

Now I’ll share some information about the number 1187:

  • 1187 is a prime number.
  • Prime factorization: 1187 is prime.
  • The exponent of prime number 1187 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1187 has exactly 2 factors.
  • Factors of 1187: 1, 1187
  • Factor pairs: 1187 = 1 × 1187
  • 1187 has no square factors that allow its square root to be simplified. √1187 ≈ 34.45287

How do we know that 1187 is a prime number? If 1187 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1187 ≈ 34.5. Since 1187 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1187 is a prime number.

1187 is the sum of the nineteen prime numbers from 23 to 103.
It is also the sum of three consecutive primes:
389 + 397 + 401 = 1187

1181 and Level 5

Some parts of this puzzle are easier than others, but it all still a lot of fun! Give it a try and enjoy yourself!

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

Now I’ll share some facts about the number 1181:

  • 1181 is a prime number.
  • Prime factorization: 1181 is prime.
  • The exponent of prime number 1181 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1181 has exactly 2 factors.
  • Factors of 1181: 1, 1181
  • Factor pairs: 1181 = 1 × 1181
  • 1181 has no square factors that allow its square root to be simplified. √1181 ≈ 34.36568

How do we know that 1181 is a prime number? If 1181 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1181 ≈ 34.4. Since 1181 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1181 is a prime number.

34² + 5² = 1181

1181 is the hypotenuse of a Pythagorean triple:
340-1131-1181 calculated from 2(34)( 5), 34² – 5², 34² + 5²

Here’s another way we know that 1181 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 34² + 5² = 1181 with 34 and 5 having no common prime factors, 1181 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1181 ≈ 34.4. Since 1181 is not divisible by 5, 13, 17, or 29, we know that 1181 is a prime number.

1181 is also palindrome 353 in BASE 19
because 3(19²) + 5(19) + 3(1) = 1181

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

1163 and Level 2

Can you write the numbers 1 to 12 in both the first column and the top row of this puzzle so those numbers and the clues function like a multiplication table? Sure you can!

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

Here is some information about the number 1163:

  • 1163 is a prime number.
  • Prime factorization: 1163 is prime.
  • The exponent of prime number 1163 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1163 has exactly 2 factors.
  • Factors of 1163: 1, 1163
  • Factor pairs: 1163 = 1 × 1163
  • 1163 has no square factors that allow its square root to be simplified. √1163 ≈ 34.10279

How do we know that 1163 is a prime number? If 1163 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1163 ≈ 34.1. Since 1163 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1163 is a prime number.

Prime number 1163 is also the sum of nine consecutive primes:
107 + 109 + 113 + 127 + 131 +137 + 139 + 149 + 151 = 1163

1153 Level 4 Pair of Glasses

Today’s puzzle reminds me of a pair of glasses. If I misplace my glasses, it can be difficult to find them, because I can’t see well without them.  But it shouldn’t be hard to see the logic in this level 4 puzzle. Give it a try. I think you will be pleasantly surprised.

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

Now let me see what I can tell you about the number 1153:

1153 is the sum of the thirteen prime numbers from 61 to 113.

Like every other prime number ending in 52, it is the sum of two squares:
33² + 8² = 1153

1153 is the hypotenuse of a Pythagorean triple:
528-1025-1153 calculated from 2(33)(8), 33² – 8², 33² + 8²

1153 is a palindrome in two other bases:
It’s 5C5 in BASE 14 (C is 12 base 10) because 5(14²) + 12(14) + 5(1) = 1153,
and 141 in BASE 32 because 32² + 4(32) + 1 = 1153

1151 and Level 3

If you know the common prime factor for 27 and 30, then you can at least start this puzzle. If you work down the first column cell by cell using logic, you should be able to solve the puzzle, too. Good luck!

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

Here are some facts about the number 1151:

  • 1151 is a prime number.
  • Prime factorization: 1151 is prime.
  • The exponent of prime number 1151 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1151 has exactly 2 factors.
  • Factors of 1151: 1, 1151
  • Factor pairs: 1151 = 1 × 1151
  • 1151 has no square factors that allow its square root to be simplified. √1151 ≈ 33.92639

How do we know that 1151 is a prime number? If 1151 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1151 ≈ 33.9. Since 1151 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1151 is a prime number.

1151 is the sum of consecutive primes three different ways:
It is the sum of the twenty-three prime numbers from 7 to 101.
223 + 227 + 229 + 233 + 239 = 1151 and
379 + 383 + 389 = 1151

Stetson.edu states that 1151 is the smallest number that is the sum of consecutive prime numbers four different ways, I think they must be considering 1151 = 1151 to be one of those ways.

1151 is palindrome 1L1 in BASE 25 (L is 21 base 10)
because 25² + 21(25) + 1 = 1151

1123 and Level 2

All the clues in one of the rows of this Level 2 puzzle are prime numbers. The only common factor they have is 1. That fact will get you started with this puzzle which I am sure you can complete if you just give it a try!

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

1123 is also a prime number. Here are some facts about it.

  • 1123 is a prime number.
  • Prime factorization: 1123 is prime.
  • The exponent of prime number 1123 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1123 has exactly 2 factors.
  • Factors of 1123: 1, 1123
  • Factor pairs: 1123 = 1 × 1123
  • 1123 has no square factors that allow its square root to be simplified. √1123 ≈ 33.51119

How do we know that 1123 is a prime number? If 1123 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1123 ≈ 33.5. Since 1123 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1123 is a prime number.

Stetson.edu reminds us that 1, 1, 2, 3 are the first four numbers in the Fibonacci sequence.

1123 is the sum of five consecutive prime numbers:
211 + 223 + 227 + 229 + 233 = 1123

1123 is palindrome 797 in BASE 12 because 7(12²) + 9(12) + 7(1) = 1123, and
it’s repdigit 111 in BASE 33 because 33² + 33 + 1 = 1123

1117 and Level 5

Can you solve this Level 5 puzzle or will it make you feel like toast? Seriously, I think it’s a little easier than the previous puzzle, so give it a try. You might just become the toast of the town!

Print the puzzles or type the solution in this excel file: 12 factors 1111-1119

Now I’ll share some information about the number 1117:

  • 1117 is a prime number.
  • Prime factorization: 1117 is prime.
  • The exponent of prime number 1117 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1117 has exactly 2 factors.
  • Factors of 1117: 1, 1117
  • Factor pairs: 1117 = 1 × 1117
  • 1117 has no square factors that allow its square root to be simplified. √1117 ≈ 33.42155

How do we know that 1117 is a prime number? If 1117 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1117 ≈ 33.4. Since 1117 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1117 is a prime number.

26² + 21² = 1117

1117 is the hypotenuse of a Pythagorean triple:
235-1092-1117 calculated from 26² – 21², 2(26)(21), 26² + 21²

Here’s another way we know that 1117 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 26² + 21² = 1117 with 26 and 21 having no common prime factors, 1117 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1117 ≈ 33.4. Since 1117 is not divisible by 5, 13, 17, or 29, we know that 1117 is a prime number.

1117 is palindrome 151 in BASE 31 because 1(31²) + 5(31) + 1(1) = 1117

1103 and Level 2

The fourteen clues you see in this puzzle are all you need to find all the factors from 1 to 10 and complete the multiplication table. Can you find all those factors?

Print the puzzles or type the solution in this excel file: 10-factors-1102-1110

Here are some facts about the number 1103:

  • 1103 is a prime number.
  • Prime factorization: 1103 is prime.
  • The exponent of prime number 1103 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1103 has exactly 2 factors.
  • Factors of 1103: 1, 1103
  • Factor pairs: 1103 = 1 × 1103
  • 1103 has no square factors that allow its square root to be simplified. √1103 ≈ 33.21144

How do we know that 1103 is a prime number? If 1103 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1103 ≈ 33.2. Since 1103 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1103 is a prime number.

1103 is the sum of the nineteen prime numbers from 19 to 101.

1103 is palindrome 191 in BASE 29 because 1(29²) + 9(29) + 1(1) = 1103