Puzzles

1269 Tangram Witch Puzzle

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If you have the seven tangram pieces, then you can create this Halloween witch riding across the moon (or a paper plate). Best Witches creating all kinds of things with those fabulous tiles!

In case you would like to know some facts about the number 1269, here’s what I’ve learned:

  • 1269 is a composite number.
  • Prime factorization: 1269 = 3 × 3 × 3 × 47, which can be written 1269 = 3³ × 47
  • 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 1269 has exactly 8 factors.
  • Factors of 1269: 1, 3, 9, 27, 47, 141, 423, 1269
  • Factor pairs: 1269 = 1 × 1269, 3 × 423, 9 × 141, or 27 × 47
  • Taking the factor pair with the largest square number factor, we get √1269 = (√9)(√141) = 3√141 ≈ 35.62303

1269 is the difference of two squares four different ways:
37² – 10² = 1269
75² – 66² = 1269
213² – 210² = 1269
635² – 634² = 1269

1268 Halloween Cat Mystery

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Cats can be quite mysterious. They are a favorite pet for many every day, even though suspicious stories abound about them on Halloween. Can you solve the mystery of this cat-like puzzle?

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Now I’ll share a few facts about the number 1268:

  • 1268 is a composite number.
  • Prime factorization: 1268 = 2 × 2 × 317, which can be written 1268 = 2² × 317
  • 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 1268 has exactly 6 factors.
  • Factors of 1268: 1, 2, 4, 317, 634, 1268
  • Factor pairs: 1268 = 1 × 1268, 2 × 634, or 4 × 317
  • Taking the factor pair with the largest square number factor, we get √1268 = (√4)(√317) = 2√317 ≈ 35.60899

28² + 22² = 1268

1268 is the hypotenuse of a Pythagorean triple:
300-1232-1268 calculated from 28² – 22², 2(28)(22), 28² + 22².
It is also 4 times (75-308-317)

1267 Frankenstein Mystery

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There are legends of Dr. Frankenstein creating a monster years ago. Nowadays Frankenstein’s Monster can often be seen walking through neighborhoods on Halloween night. This puzzle looks a little bit like him.

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

But if you take all the color away, he looks completely different and quite harmless:

Now I’ll share some information about the number 1267:

  • 1267 is a composite number.
  • Prime factorization: 1267 = 7 × 181
  • 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 1267 has exactly 4 factors.
  • Factors of 1267: 1, 7, 181, 1267
  • Factor pairs: 1267 = 1 × 1267 or 7 × 181
  • 1267 has no square factors that allow its square root to be simplified. √1267 ≈ 35.59494

1267 is the sum of nine consecutive prime numbers:
113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 = 1267

1267 is the hypotenuse of a Pythagorean triple:
133-1260-1267 which is 7 times (19-180-181)

 

1265 More Candy Corn

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People don’t each candy corn every day and the only corn in it is corn syrup.  We usually only see it this time of year. Here’s a puzzle with some candy corn for you to enjoy:

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

  • 1265 is a composite number.
  • Prime factorization: 1265 = 5 × 11 × 23
  • 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 1265 has exactly 8 factors.
  • Factors of 1265: 1, 5, 11, 23, 55, 115, 253, 1265
  • Factor pairs: 1265 = 1 × 1265, 5 × 253, 11 × 115, or 23 × 55
  • 1265 has no square factors that allow its square root to be simplified. √1265 ≈ 35.56684

1265 is the sum of the fifteen prime numbers from 53 to 113.

1265 is the hypotenuse of a Pythagorean triple:
759-1012-1265 which is (3-4-5) times 253

1264 Dum Dums Mystery

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Dum Dums have been around since 1924. If you go trick or treating, you will likely get at least one of these popular lollipops. Have fun solving the Dum Dums mystery puzzle I’ve made for you.

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Here are a few facts about the number 1264:

  • 1264 is a composite number.
  • Prime factorization: 1264 = 2 × 2 × 2 × 2 × 79, which can be written 1264 = 2⁴ × 79
  • The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 × 2 = 10. Therefore 1264 has exactly 10 factors.
  • Factors of 1264: 1, 2, 4, 8, 16, 79, 158, 316, 632, 1264
  • Factor pairs: 1264 = 1 × 1264, 2 × 632, 4 × 316, 8 × 158, or 16 × 79
  • Taking the factor pair with the largest square number factor, we get √1264 = (√16)(√79) = 4√79 ≈ 35.55278

1264 is the sum of the first twenty-seven prime numbers. That’s all the prime numbers from 2 to 103.

 

 

1263 Candy Corn Mystery

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Candy Corn is a soft traditional Halloween candy. I hope this puzzle is a sweet treat for you to solve! Just write the numbers from one to 10 in the first column and the top row so that the puzzle becomes a sort of multiplication table with the given clues becoming the products of the factors you write.

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Now I’ll write a little bit about the number 1263:

  • 1263 is a composite number.
  • Prime factorization: 1263 = 3 × 421
  • 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 1263 has exactly 4 factors.
  • Factors of 1263: 1, 3, 421, 1263
  • Factor pairs: 1263 = 1 × 1263 or 3 × 421
  • 1263 has no square factors that allow its square root to be simplified. √1263 ≈ 35.53871

1263 is the hypotenuse of a Pythagorean triple:
87-1260-1263 which is 3 times (29-420-421)

1262 Jack-o-lantern Mystery

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I have a week’s worth of Halloween themed mystery level puzzles starting with this jack-o-lantern. Mystery level doesn’t mean it’s difficult, only that I’m not letting you know if it’s tricky or not. You may find this puzzle is a real treat, so give it a try!

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Here are a few facts about the number 1262:

  • 1262 is a composite number.
  • Prime factorization: 1262 = 2 × 631
  • 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 1262 has exactly 4 factors.
  • Factors of 1262: 1, 2, 631, 1262
  • Factor pairs: 1262 = 1 × 1262 or 2 × 631
  • 1262 has no square factors that allow its square root to be simplified. √1262 ≈ 35.52464

1262 is the sum of the twenty-six prime numbers from 3 to 103.

 

1259 Graveyard Marker

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This is the first of a week’s worth of Halloween Find the Factors puzzles. Graveyards are often associated with the holiday. Many graveyards have crosses marking the place where some dearly loved person was laid to rest. This puzzle isn’t very scary. Have fun solving it!

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Now I’ll share some facts about the number 1259:

  • 1259 is a prime number.
  • Prime factorization: 1259 is prime.
  • The exponent of prime number 1259 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1259 has exactly 2 factors.
  • Factors of 1259: 1, 1259
  • Factor pairs: 1259 = 1 × 1259
  • 1259 has no square factors that allow its square root to be simplified. √1259 ≈ 35.48239

How do we know that 1259 is a prime number? If 1259 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1259 ≈ 35.5. Since 1259 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1259 is a prime number.

1259 is the sum of the twenty-five prime numbers from 5 to 103.

The number after 1259 has thirty-six factors. No wonder 1259 had to settle for 1 and itself being its only factors.

Between prime numbers 1237 and 1277, there are 39 numbers but only two of them are prime numbers. 1259 is one of them. Up to 1277 on the number line, no other segment of the same length has a lower incidence of prime numbers than that!

1258 Mystery Level

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This mystery level puzzle might start off easy enough, but before too long it will surely be a mystery what your next step should be. Don’t worry, logic can still lead the way on every step, but finding the logic might be trickier than usual.

Print the puzzles or type the solution in this excel file: 12 factors 1251-1258

Here’s some information about the number 1258:

  • 1258 is a composite number.
  • Prime factorization: 1258 = 2 × 17 × 37
  • 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 1258 has exactly 8 factors.
  • Factors of 1258: 1, 2, 17, 34, 37, 74, 629, 1258
  • Factor pairs: 1258 = 1 × 1258, 2 × 629, 17 × 74, or 34 × 37
  • 1258 has no square factors that allow its square root to be simplified. √1258 ≈ 35.4683

1258 is the sum of two squares in two different ways:
27² + 23² = 1258
33² + 13² = 1258

1258 is the hypotenuse of FOUR Pythagorean triples:
200-1242-1258
408-1190-1258
592-1110-1258
858-920-1258

1257 and Level 6

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Both 6 and 12 are allowable common factors of 60 and 12. Likewise, both 8 and 12 are allowable common factors of 96 and 72. In each case, only one of those common factors will work with this puzzle. Don’t guess and check each one. Study the other clues and at least one wrong common factor will be eliminated. Have fun solving it!

Print the puzzles or type the solution in this excel file: 12 factors 1251-1258

Now I’ll write a few things about the number 1257:

  • 1257 is a composite number.
  • Prime factorization: 1257 = 3 × 419
  • 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 1257 has exactly 4 factors.
  • Factors of 1257: 1, 3, 419, 1257
  • Factor pairs: 1257 = 1 × 1257 or 3 × 419
  • 1257 has no square factors that allow its square root to be simplified. √1257 ≈ 35.4542

1257 is the difference of two squares two different ways:
211² – 208² = 1257
629² – 628² = 1257

1257 is palindrome 393 in BASE 19