1452 Poinsettia Plant Mystery

Merry Christmas, Everybody!

The poinsettia plant has a reputation for being poisonous, but it has never been a part of a whodunnit, and it never will. Poinsettias actually aren’t poisonous.

Multiplication tables might also have a reputation for being deadly, but they aren’t either, except maybe this one. Can you use logic to solve this puzzle without it killing you?

To solve the puzzle, you will need some multiplication facts that you probably DON’T have memorized. They can be found in the table below. Be careful! The more often a clue appears, the more trouble it can be:

Notice that the number 60 appears EIGHT times in that table. Lucky for you, it doesn’t appear even once in today’s puzzle!

Now I’d like to factor the puzzle number, 1452. Here are a few facts about that number:

1 + 4 + 5 + 2 = 12, which is divisible by 3, so 1452 is divisible by 3.
1 – 4 + 5 – 2 = 0, which is divisible by 11, so 1452 is divisible by 11.

  • 1452 is a composite number.
  • Prime factorization: 1452 = 2 × 2 × 3 × 11 × 11, which can be written 1452 = 2² × 3 × 11²
  • 1452 has at least one exponent greater than 1 in its prime factorization so √1452 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1452 = (√484)(√3) = 22√3
  • The exponents in the prime factorization are 2, 1, and 2. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(2 + 1) = 3 × 2 × 3 = 18. Therefore 1452 has exactly 18 factors.
  • The factors of 1452 are outlined with their factor pair partners in the graphic below.

To commemorate the season, here’s a factor tree for 1452:

Have a very happy holiday!

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1450 A Pair of Factor Trees

On today’s puzzle, there are two small Christmas trees. Will two smaller trees on the puzzle be easier to solve than one big one? You’ll have to try it to know!

Every puzzle has a puzzle number to distinguish it from the others. Here are some facts about this puzzle number, 1450:

  • 1450 is a composite number.
  • Prime factorization: 1450 = 2 × 5 × 5 × 29, which can be written 1450 = 2 × 5² × 29
  • 1450 has at least one exponent greater than 1 in its prime factorization so √1450 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1450 = (√25)(√58) = 5√58
  • 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 1450 has exactly 12 factors.
  • The factors of 1450 are outlined with their factor pair partners in the graphic below.

In case you are looking for factor trees for 1450, here are two different ones:

1450 is the hypotenuse of SEVEN Pythagorean triples:
170-1440-1450 which is 10 times (17-144-145)
240-1430-1450 which is 10 times (24-143-145)
406-1392-1450 which is (7-24-25) times 58
666-1288-1450 which is 2 times (333-644-725)
728-1254-1450 which is 2 times (364-627-725)
870-1160-1450 which is (3-4-5) times 290
1000-1050-1450 which is (20-21-29) times 50

1447 Christmas Light Puzzle

If you’ve ever had a string of lights go out because ONE bulb went bad, it can be a very frustrating puzzle to figure out which light is causing the problem.

This is not that kind of puzzle. For this one, you just need to figure out where to put the numbers from 1 to 12 in both the first column and the top row so that the given clues are the products of those numbers. There is only one solution, and if you always use logic, it will not be a frustrating puzzle to solve.

I gave that puzzle the puzzle number 1447. That number won’t help you solve the puzzle, but here are some facts about it anyway:

  • 1447 is a prime number.
  • Prime factorization: 1447 is prime.
  • 1447 has no exponents greater than 1 in its prime factorization, so √1447 cannot be simplified.
  • The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1447 has exactly 2 factors.
  • The factors of 1447 are outlined with their factor pair partners in the graphic below.

How do we know that 1447 is a prime number? If 1447 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1447. Since 1447 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, or 37, we know that 1447 is a prime number.

1447 is also the difference of two consecutive squares:
724² – 723² = 1447

 

 

 

1446 Peppermint Stick

Red and green striped peppermint sticks are often seen in stores and homes in December. Can you lick this peppermint stick puzzle or will you let it lick you?

The puzzle number was 1446. Here are a few facts about that number:

  • 1446 is a composite number.
  • Prime factorization: 1446 = 2 × 3 × 241
  • 1446 has no exponents greater than 1 in its prime factorization, so √1446 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1446 has exactly 8 factors.
  • The factors of 1446 are outlined with their factor pair partners in the graphic below.

1446 is also the hypotenuse of a Pythagorean triple:
720-1254-1446 which is 6 times (120-209-241)

1443 A Simple Gift for You

This level one puzzle is my simple gift to you. Yes, you can solve it, and you don’t even have to wait until December 25th to discover all the factors and products to be found inside!

That was puzzle number 1443. Here are some facts about that number.

  • 1443 is a composite number.
  • Prime factorization: 1443 = 3 × 13 × 37
  • 1443 has no exponents greater than 1 in its prime factorization, so √1443 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1443 has exactly 8 factors.
  • The factors of 1443 are outlined with their factor pair partners in the graphic below.

(38-1)(38+1) = 1443 so 1443 is one number away from 38² = 1444.

Actually, 1443 is the difference of two squares in four different ways:
38² – 1² = 1443
62²- 49² = 1443
242² – 239² = 1443
722² – 721² = 1443

1443 is the hypotenuse of FOUR Pythagorean triples:
93-1440-1443 which is 3 times (31-480-481)
468-1365-1443 which is (12-35-37) times 39
555-1332-1443 which is (5-12-13) times 111
957-1080-1443 which is 3 times(319-360-481)

1439 and Level 6

You know the factors of 49, but to complete this puzzle, you will also have to determine the answers to a few questions:

Will the common factor of 24 and 32 be 4 or 8?
Will the common factor of 20 and 40 be 4, 5, or 10?
Will the common factor of 27 and 9 be 3 or 9?

Don’t guess and check! Look at the other clues, and some of the possibilities will be eliminated*. Once you’ve found the next clue to use, continue using logic until the whole puzzle is completed.

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

  • 1439 is a prime number.
  • Prime factorization: 1439 is prime.
  • 1439 has no exponents greater than 1 in its prime factorization, so √1439 cannot be simplified.
  • The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1439 has exactly 2 factors.
  • The factors of 1439 are outlined with their factor pair partners in the graphic below.

How do we know that 1439 is a prime number? If 1439 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1439. Since 1439 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, or 37, we know that 1439 is a prime number.

* Did you notice that either one of the 24’s or 6 must use a 3 because only two 6s are allowed to be used as factors? What does that tell you about the common factor of 27 and 9?

 

1438 and Level 5

You can solve this puzzle by using logic and multiplication/division facts. The unique solution requires all the numbers from 1 to 10 in both the first column and the top row. Can you solve it?

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

Today’s puzzle was given the number 1438. Here are a few facts about that number:

  • 1438 is a composite number.
  • Prime factorization: 1438 = 2 × 719
  • 1438 has no exponents greater than 1 in its prime factorization, so √1438 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 1438 has exactly 4 factors.
  • The factors of 1438 are outlined with their factor pair partners in the graphic below.

1438 is the sum of four consecutive numbers:
358  + 359 + 360 + 361 = 1438

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

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

I enjoyed this tweet from Robin Schwartz. Spoiler alert: If you click on the link, you will see the solution.

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

 

1435 is the 23rd Friedman Number

41 ×35 = 1435. Since the same digits are used on both sides of the equal sign that makes 1435 the 23rd Friedman number.

Since it’s good for puzzles to have a puzzle number to distinguish them from each other, I’ve given this one the number 1435. Can you solve it?

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

Here are a few more facts about the number 1435:

  • 1435 is a composite number.
  • Prime factorization: 1435 = 5 × 7 × 41
  • 1435 has no exponents greater than 1 in its prime factorization, so √1435 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1435 has exactly 8 factors.
  • The factors of 1435 are outlined with their factor pair partners in the graphic below.

1435 is also the hypotenuse of FOUR Pythagorean triples:
315-1400-1435 which is 35 times (9-40-41)
588-1309-1435 which is 7 times (84-187-205)
861-1148-1435 which is (3-4-5) times 287
931-1092-1435 which is 7 times (133-156-205)