1196 and Level 6

In this puzzle, the permissible common factors of 48 and 72 are 6, 8, and 12. For clues 8 and 16, you can choose from common factors 2, 4, or 8. Which choices will make the puzzle work? I’m not telling, but I promise that the entire puzzle can be solved using logic and a basic knowledge of a 12×12 multiplication table. There is only one solution.

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

Here are some facts about the number 1196:

  • 1196 is a composite number.
  • Prime factorization: 1196 = 2 × 2 × 13 × 23, which can be written 1196 = 2² × 13 × 23
  • 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 1196 has exactly 12 factors.
  • Factors of 1196: 1, 2, 4, 13, 23, 26, 46, 52, 92, 299, 598, 1196
  • Factor pairs: 1196 = 1 × 1196, 2 × 598, 4 × 299, 13 × 92, 23 × 52, or 26 × 46
  • Taking the factor pair with the largest square number factor, we get √1196 = (√4)(√299) = 2√299 ≈ 34.58323

1196 is the hypotenuse of a Pythagorean triple:
460-1104-1196 which is (5-12-13) times 92

1196 is a palindrome in three different bases:
It’s 14241 in BASE 5,
838 in BASE 12, and
616 in BASE 14

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1195 You Can Find the Answer in This Book

The new school year is underway. Much may have been forgotten over the summer. If you don’t quite remember all the multiplication tables, this puzzle book can help you remember them AND help your brain grow. You might still find it a challenge, but that only makes it more fun!

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

Now I’ll share a few facts about the number 1195:

  • 1195 is a composite number.
  • Prime factorization: 1195 = 5 × 239
  • 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 1195 has exactly 4 factors.
  • Factors of 1195: 1, 5, 239, 1195
  • Factor pairs: 1195 = 1 × 1195 or 5 × 239
  • 1195 has no square factors that allow its square root to be simplified. √1195 ≈ 34.56877

1195 is also the hypotenuse of a Pythagorean triple:
717-956-1195 which is (3-4-5) times 239

1194 and Level 4

The more multiplication facts you know, the easier these puzzles become. Working on these puzzles can help you learn the multiplication table better. Go ahead,  give this puzzle a try!

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

Here are a few facts about the number 1194:

  • 1194 is a composite number.
  • Prime factorization: 1194 = 2 × 3 × 199
  • 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 1194 has exactly 8 factors.
  • Factors of 1194: 1, 2, 3, 6, 199, 398, 597, 1194
  • Factor pairs: 1194 = 1 × 1194, 2 × 597, 3 × 398, or 6 × 199
  • 1194 has no square factors that allow its square root to be simplified. √1194 ≈ 34.5543

1194 is the sum of consecutive prime numbers two ways:
131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 = 1194
283 + 293 + 307 + 311 = 1194

1194 is palindrome 424 in BASE 17

 

1192 Experiential Learning Helps Students Understand Their Capacity

Sara Van Der Werf inspired me last year with her post titled Why You Need a PLAY TABLE in your mathematics classroom ASAP. I’ve seen merit in using play to teach and learn mathematics for some time now. What Sara’s post did was make me long to be back in a mathematics classroom so I could have such a play table!

Last week I started working at the American Academy of Innovation, a charter school near that engages students in learning through projects and other activities.

Each member of the faculty was given the assignment to make something that reflects his or her teaching philosophy. Here’s the one I put together:

On my display, I included the words, “Experiential Learning Helps Students Understand Their Capacity.” That’s my teaching philosophy.

The wording I used was intentional.

  •  “Their” might refer to the students or to the geometric solids.
  • “Capacity” has two appropriate definitions stated so perfectly by Google in the screenshot below:
    1) the ability or power the students “have to do, experience, or understand something”, and 2) the maximum amount the geometric solids can contain.

The scattered rice symbolizes that these learning experiences can sometimes be messy. We will learn more if we aren’t afraid to make mistakes or a little mess.

I am so excited! I’ve taken all my math toys out of storage and will have an ever-changing play table in my classroom where students can play and learn mathematics. Thank you, Sara Van Der Werf for inspiring me!

Now I’ll write a little about the number 1192:

  • 1192 is a composite number.
  • Prime factorization: 1192 = 2 × 2 × 2 × 149, which can be written 1192 = 2³ × 149
  • 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 1192 has exactly 8 factors.
  • Factors of 1192: 1, 2, 4, 8, 149, 298, 596, 1192
  • Factor pairs: 1192 = 1 × 1192, 2 × 596, 4 × 298, or 8 × 149
  • Taking the factor pair with the largest square number factor, we get √1192 = (√4)(√298) = 2√298 ≈ 34.52535

1192 is the sum of two consecutive prime numbers:
593 + 599 = 1192

34² +  6² = 1192

1192 is the hypotenuse of a Pythagorean triple:
408-1120-1192 calculated from 2(34)( 6), 34² –  6², 34² +  6²
It is also 8 times (51-140-149)

1192 is a cool-looking 3322 in BASE 7

1191 Happy Birthday, Brent

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

1190 and Level 3

The common factors of 108 and 120 are 1, 2, 3, 4, 6, and 12, but pick the one that will only put numbers from 1 to 12 in the first column. Then work down that first column cell by cell writing in the factors of the clues as you go. Each number from 1 to 12 must go somewhere in both the first column and the top row.

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

Now I’ll share some information about the number 1190:

  • 1190 is a composite number.
  • Prime factorization: 1190 = 2 × 5 × 7 × 17
  • The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 110. Therefore 1190 has exactly 110 factors.
  • Factors of 1190: 1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190
  • Factor pairs: 1190 = 1 × 1190, 2 × 595, 5 × 238, 7 × 170, 10 × 119, 14 × 85, 17 × 70, or 34 × 35
  • 1190 has no square factors that allow its square root to be simplified. √1190 ≈ 34.49638

Because 1190 is the product of consecutive numbers 34 and 35, we know it is the sum of the first 34 EVEN numbers. Instead of writing all of those 34 numbers, we can use a some mathematical shorthand and simply write:
2 + 4 + 6 + 8 + . . . + 64 + 66 + 68 = 1190

1190 is the hypotenuse of FOUR Pythagorean triples:
182-1176-1190 which is 14 times (13-84-85)
504-1078-1190 which is 14 times (36-77-85)
560-1050-1190 which is (8-15-17) times 70
714-952-1190 which is (3-4-5) times 238

I like the way 1190 looks in some other bases:
It’s 707 in BASE 13 because 7(13²) + 7(1) = 7(169 + 1) = 7(170) = 1190,
545 in BASE 15,
2A2 in BASE 22,
1C1 in BASE 29 (C is 12 base 10),
and Y0 in BASE 35 (Y is 34 base 10) because 34(35) = 1190

1189 and Level 2

Some of the clues in this level 2 puzzle were also in the level 1 puzzle earlier this week. Can you remember their common factors and figure out the common factors for the other three sets of clues?

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

Here are some facts about the number 1189:

  • 1189 is a composite number.
  • Prime factorization: 1189 = 29 × 41
  • 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 1189 has exactly 4 factors.
  • Factors of 1189: 1, 29, 41, 1189
  • Factor pairs: 1189 = 1 × 1189 or 29 × 41
  • 1189 has no square factors that allow its square root to be simplified. √1189 ≈ 34.48188

33² + 10² = 1189
30² + 17² = 1189

1189 is the hypotenuse of FOUR Pythagorean triples:
261-1160-1189 which is 29 times (9-40-41)
611-1020-1189 calculated from 30² – 17², 2(30)(17), 30² + 17²
660-989-1189 calculated from 2(33)(10), 33² – 10², 33² + 10²
820-861-1189 which is (20-21-29) times 41

1189 is 10010100101 in BASE 2. That’s a nice pattern.
It’s also palindrome 1H1 in base 27 ( H is 17 base 10),
and palindrome 131 in BASE 33

1188 How Many Triangles? How Many Factors?

Manually counting ALL the triangles in the graphic below could get confusing. Try counting all the triangles that point up first then all the triangles that point down.

Since the number of triangle rows is an even number, you could just use this formula:

n(n+2)(2n+1)/8 = the number of triangles

In this case, n = 16, so the number of triangles is 16×18×33/8 = 1188.

(If the number of rows is an odd number, the formula produces a number with a decimal. In that case, just ignore the decimal and everything after it to get the number of triangles.)

Here’s some more information about the number 1188:

  • 1188 is a composite number.
  • Prime factorization: 1188 = 2 × 2 × 3 × 3 × 3 × 11, which can be written 1188 = 2² × 3³ × 11
  • The exponents in the prime factorization are 2, 3 and 1. Adding one to each and multiplying we get (2 + 1)(3 + 1)(1 + 1) = 3 × 4 × 2 = 24. Therefore 1188 has exactly 24 factors.
  • Factors of 1188: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 99, 108, 132, 198, 297, 396, 594, 1188
  • Factor pairs: 1188 = 1 × 1188, 2 × 594, 3 × 396, 4 × 297, 6 × 198, 9 × 132, 11 × 108, 12 × 99, 18 × 66, 22 × 54, 27 × 44 or 33 × 36
  • Taking the factor pair with the largest square number factor, we get √1188 = (√36)(√33) = 6√33 ≈ 34.46738

1188 has MANY possible factor trees. Here are four of them:

1188 is an interesting-looking base 10 number, but it also looks interesting when it is written in some other bases:
It’s 2244 in BASE 8,
990 in BASE 11 because 9(11²) + 9(11) = 9(132) = 1188,
543 in BASE 15,
4A4 in BASE 16 (A is 10 base 10),
XX in BASE 35 (X is 33 base 10) because 33(35) + 33(1) = 33(36) = 1188,
and it’s X0 in BASE 36 because 33(36) = 1188

1186 Challenge Puzzle

It shouldn’t be too hard to make your first move in this puzzle. After that, I don’t make any guarantees. You just need to write each number from 1 to 10 in each of the four boldly outlined areas so that the given clues are the products of the factors you wrote. Use logic to find all the factors and have fun doing it!

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

What have I found out about the number 1186?

  • 1186 is a composite number.
  • Prime factorization: 1186 = 2 × 593
  • 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 1186 has exactly 4 factors.
  • Factors of 1186: 1, 2, 593, 1186
  • Factor pairs: 1186 = 1 × 1186 or 2 × 593
  • 1186 has no square factors that allow its square root to be simplified. √1186 ≈ 34.43835

31² + 15² = 1186

1186 is the hypotenuse of a Pythagorean triple:
736-930-1186 calculated from 31² – 15², 2(31)(15), 31² + 15²

1186 is palindrome 989 in BASE 11

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