1437 Belt Buckle Mystery

I have childhood memories of preparing for Thanksgiving at school by making pilgrim hats, pilgrim shirts, or pilgrim shoes out of construction paper. Each of those clothing items had a distinguished buckle. Why? That buckle’s popularity was a mystery to me until I read an article by Ken Jennings titled The Debunker: What Did Pilgrim Hats Really Look Like?

This mystery level puzzle has a buckle, too. Perhaps it can help debunk the idea that math is no fun while it helps you learn about factors or reinforces your memory of the multiplication table.

Print the puzzles or type the solution in this excel file:  10 Factors 1432-1442

The puzzle number is 1437. Here are a few facts about that number:

  • 1437 is a composite number.
  • Prime factorization: 1437 = 3 × 479
  • 1437 has no exponents greater than 1 in its prime factorization, so √1437 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1437 has exactly 4 factors.
  • The factors of 1437 are outlined with their factor pair partners in the graphic below.

1437 is the difference of two squares in two different ways:
719² – 718² = 1437
241² – 238² = 1437

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1436 This Turkey Is Ready

If this year you find yourself needing a bigger turkey, then this one fits that description. This turkey uses math facts from a 14 × 14 multiplication table.

Adding prime number 13 doesn’t cause any problems. You hopefully will recognize that 39 and 119 are both multiples of 13.

However, adding 14 to the puzzle might make you want to call “fowl” because clues 28, 56, 70, and 84 all have two sets of factor pairs where both factors are 14 or less. Can you figure out which clues use 7 and which use 14?

Like always, there is only one solution.

Print the puzzles or type the solution in this excel file:  10 Factors 1432-1442

That was puzzle number 1436. Here are a few facts about that number:

  • 1436 is a composite number.
  • Prime factorization: 1436 = 2 × 2 × 359, which can be written 1436 = 2² × 359
  • 1436 has at least one exponent greater than 1 in its prime factorization so √1436 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1436 = (√4)(√359) = 2√359
  • The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1436 has exactly 6 factors.
  • The factors of 1436 are outlined with their factor pair partners in the graphic below.

1436 is the difference of two squares:
360² – 358² = 1436

1427 Mysterious Cat

This mysterious Halloween cat shares twelve clues that can help you solve its puzzle. Each clue is the products of two factors from 1 to 12 multiplied together. Will you be able to solve its mystery?

Print the puzzles or type the solution in this excel file: 12 Factors 1419-1429

Now I’ll tell you a little bit about the puzzle number, 1427:

  • 1427 is a prime number.
  • Prime factorization: 1427 is prime.
  • 1427 has no exponents greater than 1 in its prime factorization, so √1427 cannot be simplified.
  • The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1427 has exactly 2 factors.
  • The factors of 1427 are outlined with their factor pair partners in the graphic below.

How do we know that 1427 is a prime number? If 1427 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1427. Since 1427 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, or 37, we know that 1427 is a prime number.

1427 is 272 in BASE 25 because 2(25²) + 7(25) + 2(1) = 1427

1425 Jack O’Lantern

Most of my puzzles don’t have as many clues as this Jack O’lantern puzzle has. Those extra clues could make it easier to solve. On the other hand, some of the clues might still be tricky.

Print the puzzles or type the solution in this excel file: 12 Factors 1419-1429

Here are some facts about the puzzle number, 1425:

  • 1425 is a composite number.
  • Prime factorization: 1425 = 3 × 5 × 5 × 19, which can be written 1425 = 3 × 5² × 19
  • 1425 has at least one exponent greater than 1 in its prime factorization so √1425 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1425 = (√25)(√57) = 5√57
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each exponent and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1425 has exactly 12 factors.
  • The factors of 1425 are outlined with their factor pair partners in the graphic below.

1425 is the hypotenuse of TWO Pythagorean triples:
399-1368-1425 which is (7-24-25) times 57
855-1140-1425 which is (3-4-5) times 285

 

1422 Candy Corn Mystery

You can begin this candy corn puzzle easily enough, but the logic needed to solve it is a bit complicated. Good luck with this one!

Print the puzzles or type the solution in this excel file: 12 Factors 1419-1429

Now I’ll tell you some facts about the puzzle number, 1422:

  • 1422 is a composite number.
  • Prime factorization: 1422 = 2 × 3 × 3 × 79, which can be written 1422 = 2 × 3² × 79
  • 1422 has at least one exponent greater than 1 in its prime factorization so √1422 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1422 = (√9)(√158) = 3√158
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each exponent and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1422 has exactly 12 factors.
  • The factors of 1422 are outlined with their factor pair partners in the graphic below.

1422 is palindrome 1K1 in BASE 29 (K is 20 base 10)
because 1(29²) + 20(29¹) + 1(29º) = 1422.

1417 Mystery Puzzle

How hard is today’s puzzle? It’s a little harder just because I’m not telling what the level number is. Are you going to let that stop you from finding the unique solution? I hope not!

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

1417 is just the puzzle number, but in case you want to know something about it, here are some facts:

  • 1415 is a composite number.
  • Prime factorization: 1415 = 13 × 109
  • 1415 has no exponents greater than 1 in its prime factorization, so √1415 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1415 has exactly 4 factors.
  • The factors of 1415 are outlined with their factor pair partners in the graphic below.

1417 is the sum of two squares in two different ways:
29² + 24² = 1417
36² + 11² = 1417

1417 is the hypotenuse of FOUR Pythagorean triples:
265-1392-1417 calculated from 29² – 24², 2(29)(24), 29² + 24²
545-1308-1417 which is (5-12-13) times 109
780-1183-1417 which is 13 times (60-91-109)
792-1175-1417 calculated from 2(36)(11) , 36² – 11² , 36² + 11²

1416 A Birthday Mystery

Today is my sister’s birthday, but the cake is tipped over and there’s a big hole in it! And what happened to the candle? Can you solve this mystery? Happy birthday, Sue!


Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Now I’ll share some facts about the puzzle number 1416:

  • 1416 is a composite number.
  • Prime factorization: 1416 = 2 × 2 × 2 × 3 × 59, which can be written 1416 = 2³ × 3 × 59
  • 1416 has at least one exponent greater than 1 in its prime factorization so √1416 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1416 = (√4)(√354) = 2√354
  • The exponents in the prime factorization are 3,1 and 1. Adding one to each exponent and multiplying we get (3 + 1)(1 + 1) (1 + 1) = 4 × 2 × 2 = 16. Therefore 1416 has exactly 16 factors.
  • The factors of 1416 are outlined with their factor pair partners in the graphic below.

1416 is the difference of two squares four ways:
355² – 353²  = 1416
179² – 175²  = 1416
121² – 115²  = 1416
65² – 53²  = 1416

1402 Mystery Level

Mystery level puzzles may be very difficult or relatively easy. How much trouble will this one be? You’ll have to try it to see!

Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll tell you a little bit about the number 1402:

  • 1402 is a composite number.
  • Prime factorization: 1402 = 2 × 701
  • 1402 has no exponents greater than 1 in its prime factorization, so √1402 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1402 has exactly 4 factors.
  • The factors of 1402 are outlined with their factor pair partners in the graphic below.

1402 is the hypotenuse of a Pythagorean triple:
31² + 21² = 1402

1402 is the hypotenuse of a Pythagorean triple:
520-1302-1402 which is 2 times (260-651-701)
and can also be calculated from 2(31)(21), 31² – 21², 31² + 21²

1401 Roasting Over an Open Fire

I went camping last week. My family roasted hotdogs. Some people refer to them as mystery meat. Others roasted marshmallows. I was surprised to learn that almost all brands of marshmallows have blue dye in them.  I’m told that without that blue dye the marshmallows will lose their whiteness as they sit on store shelves. Why they have to be that white is a mystery to me.

Here’s a mystery level puzzle for you to solve. It looks a lot like the utensil that was used to roast the hotdogs and marshmallows.

Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll tell you something about the number 1401:

  • 1401 is a composite number.
  • Prime factorization: 1401 = 3 × 467
  • 1401 has no exponents greater than 1 in its prime factorization, so √1401 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1401 has exactly 4 factors.
  • The factors of 1401 are outlined with their factor pair partners in the graphic below.

1401 is the difference of two squares in two different ways. Can you figure out what those ways are?

1388 Mystery Level

Sometimes puzzles start out easy enough but get a little more complicated later on. Does that happen with this puzzle? There’s only one way to find out!


Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Here are some facts about the number 1388:

  • 1388 is a composite number.
  • Prime factorization: 1388 = 2 × 2 × 347, which can be written 1388 = 2² × 347
  • 1388 has at least one exponent greater than 1 in its prime factorization so √1388 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1388 = (√4)(√347) = 2√347
  • The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1388 has exactly 6 factors.
  • The factors of 1388 are outlined with their factor pair partners in the graphic below.

1388 is the difference of two squares:
348² – 346² = 1388