1325 Hockey Stick

If someone you know loves hockey and wants a fun way to practice multiplication facts, this hockey stick could be the perfect gift.

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1246 and Level 4

The reason level 4 puzzles are more difficult than level 3 puzzle is that you have to look all over the puzzle to find the next clue that will help you solve it. Still, there are only 10 clues in this puzzle, so you don’t have to look in very many places. Go ahead and give this puzzle a try!

Print the puzzles or type the solution in this excel file: 10-factors-1242-1250

Let me share some facts about the number 1246:

  • 1246 is a composite number.
  • Prime factorization: 1246 = 2 × 7 × 89
  • 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 1246 has exactly 8 factors.
  • Factors of 1246: 1, 2, 7, 14, 89, 178, 623, 1246
  • Factor pairs: 1246 = 1 × 1246, 2 × 623, 7 × 178, or 14 × 89
  • 1246 has no square factors that allow its square root to be simplified. √1246 ≈ 35.29873

1246 is the hypotenuse of a Pythagorean triple:
546-1120-1246 which is 14 times (39-80-89)

1236 and Level 4

V is for victory. Can you be victorious solving this puzzle? Write the numbers from 1 to 12 in both the first column and the top row so that the puzzle functions like a multiplication table with the given clues becoming the products of the factors you write. I’m sure you can do it if you stick with it!

Print the puzzles or type the solution in this excel file: 12 factors 1232-1241

Now I’ll tell you some facts about the number 1236:

  • 1236 is a composite number.
  • Prime factorization: 1236 = 2 × 2 × 3 × 103, which can be written 1236 = 2² × 3 × 103
  • 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 1236 has exactly 12 factors.
  • Factors of 1236: 1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, 1236
  • Factor pairs: 1236 = 1 × 1236, 2 × 618, 3 × 412, 4 × 309, 6 × 206, or 12 × 103
  • Taking the factor pair with the largest square number factor, we get √1236 = (√4)(√309) = 2√309 ≈ 35.15679

1236 is the sum of consecutive prime numbers three rather interesting ways:

  1. It is the sum of the twenty-two prime numbers from 13 to 103.
  2. It is the sum of the eight prime numbers from 137 to 173.
    (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 = 1236)
  3. It is also the sum of twin primes: 617 + 619 = 1236

1227 and Level 4

I’m confident you know a common factor of 42 and 60 for which ALL the factors involved are numbers from 1 to 10. That’s all you need to know to start this puzzle. Go ahead, give it a try!

Print the puzzles or type the solution in this excel file: 10-factors-1221-1231

Here is some information about the number 1227:

  • 1227 is a composite number.
  • Prime factorization: 1227 = 3 × 409
  • 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 1227 has exactly 4 factors.
  • Factors of 1227: 1, 3, 409, 1227
  • Factor pairs: 1227 = 1 × 1227 or 3 × 409
  • 1227 has no square factors that allow its square root to be simplified. √1227 ≈ 35.02856

1227 is the hypotenuse of a Pythagorean triple:
360-1173-1227 which is 3 times (120-391-409)

 

1214 and Level 4

Even though I don’t tell you the order to consider the clues in today’s puzzle, you can still solve it. Just use logic and your knowledge of a standard 12 × 12 multiplication table to find its unique solution. Good luck!

Print the puzzles or type the solution in this excel file: 12 factors 1211-1220

Now I’ll share a few facts about the number 1214:

  • 1214 is a composite number.
  • Prime factorization: 1214 = 2 × 607
  • 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 1214 has exactly 4 factors.
  • Factors of 1214: 1, 2, 607, 1214
  • Factor pairs: 1214 = 1 × 1214 or 2 × 607
  • 1214 has no square factors that allow its square root to be simplified. √1214 ≈ 34.8425

1214 is the sum of six consecutive prime numbers:
191 + 193 + 197 + 199 + 211 + 223 = 1214

1204 and Level 4

Today’s puzzle looks like a giant times table with a big X in the middle. The factors for this times table are not in the usual places. Can you figure out where they all go?

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

Here are a few facts about the number 1204:

  • 1204 is a composite number.
  • Prime factorization: 1204 = 2 × 2 × 7 × 43, which can be written 1204 = 2² × 7 × 43
  • 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 1204 has exactly 12 factors.
  • Factors of 1204: 1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204
  • Factor pairs: 1204 = 1 × 1204, 2 × 602, 4 × 301, 7 × 172, 14 × 86, or 28 × 43
  • Taking the factor pair with the largest square number factor, we get √1204 = (√4)(√301) = 2√301 ≈ 34.6987

1204 is the difference of two squares two different ways:
302² – 300² = 1204
50² – 36² = 1204

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

 

1179 and Level 4

80 and 16 have just one common factor that will put only numbers from 1 to 10 in the first column and in the top row. Put those factors where they belong and use logic to figure out where to put the rest.

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

Now I tell you what I’ve learned about the number 1179:

  • 1179 is a composite number.
  • Prime factorization: 1179 = 3 × 3 × 131, which can be written 1179 = 3² × 131
  • 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 1179 has exactly 6 factors.
  • Factors of 1179: 1, 3, 9, 131, 393, 1179
  • Factor pairs: 1179 = 1 × 1179, 3 × 393, or 9 × 131
  • Taking the factor pair with the largest square number factor, we get √1179 = (√9)(√131) = 3√131 ≈ 34.33657

I like the way 1179 looks in a couple other bases:
It’s 2233 in BASE 8 because 2(8³ + 8²) + 3(8 + 1) = 1179,
and 171 in BASE 31 because 31² + 7(31) + 1 = 1179

1166 and Level 4

Study the clues in this puzzle. Find the most logical place to start and begin there. Once you find all the factors you will see how amazing YOU are! You can do this!

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

Now I’ll share some information about the number 1166:

  • 1166 is a composite number.
  • Prime factorization: 1166 = 2 × 11 × 53
  • 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 1166 has exactly 8 factors.
  • Factors of 1166: 1, 2, 11, 22, 53, 106, 583, 1166
  • Factor pairs: 1166 = 1 × 1166, 2 × 583, 11 × 106, or 22 × 53
  • 1166 has no square factors that allow its square root to be simplified. √1166 ≈ 34.14674

1166 is the hypotenuse of a Pythagorean triple:
616-990-1166 which is 22 times (28-45-53)