## A Multiplication Based Logic Puzzle

### 338 Liebster Award or Not

• 338 is a composite number.
• Prime factorization: 338 = 2 x 13 x 13, which can be written 338 = 2 x (13^2)
• The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 x 3  = 6. Therefore 338 has exactly 6 factors.
• Factors of 338: 1, 2, 13, 26, 169, 338
• Factor pairs: 338 = 1 x 338, 2 x 169, or 13 x 26
• Taking the factor pair with the largest square number factor, we get √338 = (√2)(√169) = 13√2 ≈ 18.385

Starguy recently nominated me for this blue-green Liebster award. Many bloggers have a no award policy, and I can certainly understand why: receiving an award is a bit of work if you accept it. The Liebster award has been around for a long time, and it has been said that just about every blogger has received it at one time or another.

As these images demonstrate, some recipients have changed the way the award looks.

Since the logo has been changed multiple times by multiple people, I don’t feel bad having a somewhat rebellious attitude as I accept some of the qualifiers for the award while rejecting others. I’m not interested in sharing 11 random facts about myself, answering 11 questions, or coming up with 11 more to ask my nominees. I’m sure you will learn at least 11 things about me just reading this post anyway. (Random fact: I don’t like reading really long posts that go on forever, and this post will be long enough as it is.) If my nominees would like to write and answer questions, they can refer back to the questions asked in Starguy‘s post.

The idea of the Liebster award is to help bloggers get out of their comfort zones and discover new blogs, and I have done that. In fact several of the blogs I mention in this post I discovered within the last couple of weeks.

Rather than make a simple list of nominees, I’m going to do MORE than required and  describe one of their noteworthy posts. Hopefully the way that I do this will cause them to get a ping back notification because rebellious me is probably not going to inform them of their nominations any other way. Besides, if more people click on their links because I nominated them here, then the nomination will be meaningful. They will most likely notice when they view the referrers on their stat pages that Findthefactors is sending several people their way as well. Otherwise this nomination won’t mean much. Nevertheless, please, click on their links. Here are my 11 nominees in no particular order:

1. Even though I am an English speaking grandma, I  listened only to Hungarian Christmas carols this year. Justkinga is a Hungarian teenage girl who listens to popular English music all year long. She takes TEN classes at a bilingual school, but somehow finds the time to write a delightful blog in ENGLISH regularly. I ADMIRE HER for writing in English even if there is an occasional grammar error or incorrect word choice. She also writes about Hungarian life and culture.
2. Established1962 wrote about an ingenious way to make Snakes and Ladders a game of decision making rather than mere chance. In the process he made the game something even older players would enjoy playing while they observe some subtle mathematics.
3. Nebushumor wrote a very funny post about an extermination ad that featured an adorable Christmas mouse. Other times he’s written about Star Trek, funny family pet rabbit situations, classic cartoons, and comedy gags. Once a week he shares some kind of  humorous statistics.
4. Solvemymaths shared a great link showing multiple ways to prove the Pythagorean theorem. The 3-4-5 triangle that accompanies his post is far more than a simple illustration. Solvemymaths routinely posts a variety of math problems, gifs, computer programs, and pictures that can help you think and learn to solve your own math problems.
5. Because I am a vegetarian, I was intrigued by notquitefrenchcuisine‘s old Hungarian family recipe for vegetarian burgers. I also love that she sprinkles a few Hungarian food words in her posts, too.
6. When I first read Puzzled Over’s Ages-of-three-daughters, I wasn’t sure how the last clue could possibly help me solve it. Maybe it will stump you at first, too, but it really can be solved without too much trouble.
7. One of the topics Classy Cheapskate blogs about is minimalism. She says a comfortable minimalist owns about 150 things. I can’t imagine that being possible for ANYONE right now, but I do want to head closer to that direction as does she.
8. I loved Paula Beardell Krieg’s instructions on how to fold paper to make an-equilateral-triangle and other basic shapes. Her method uses the straight edge of a piece of paper, but no compass is needed. Elementary school children can even make perfect squares or triangles using her methods.
9. Margarita Morris  is a young adult author who has shared the complete writing process with her readers. Her books are well researched, written, and revised. She also shares her love of great classical musical and can capture a scene in nature without writing a single word.
10. Resourceaholic scours the internet for resources that teach mathematics. Every one of her posts is loaded with as much information as this link. Your students will learn more if you read her blog, and chances are you will learn something, too!
11. Nerdinthebrain is a home-schooling parent who loves science and mathematics and sharing her lessons with us. Because of her, my grandson and I had a ton of fun testing the pH of different liquids using red cabbage water. She has MANY good ideas and products.
12. The Chaos Fairy was also nominated for the Liebster Award at the same time that I was so I’m not counting this as one of my 11. Nevertheless, I just had to recognize the DINOSAUR loving in this blog post.

### 337 What Will Be the Factors of 2015?

• 337 is a prime number.
• Prime factorization: 337 is prime and cannot be factored.
• The exponent of prime number 337 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 337 has exactly 2 factors.
• Factors of 337: 1, 337
• Factor pairs: 337 = 1 x 337
• 337 has no square factors that allow its square root to be simplified. √337 ≈ 18.358

How do we know that 337 is a prime number? If 337 were not a prime number, then it would be divisible by at least one prime number less than or equal to √337 ≈ 18.358. Since 337 cannot be divided evenly by 2, 3, 5, 7, 11, 13, or 17, we know that 337 is a prime number.

WHAT will be the FACTORS of the YEAR 2015?

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

On New Year’s Eve 2013 I predicted that the positive factors for 2014 would be 1, 2, 19, 38, 53, 106,1007, and 2014, and my predictions were 100% accurate!

On this last day of 2014, I boldly announce my predictions for the factors of the year 2015:

• The positive factors for 2015 will be 1, 5, 13, 31, 65, 155, 403, and 2015
• Some of these factors will occur in pairs: 1 and 2015, 5 and 403, 13 and 155, as well as 31 and 65.
• Unfortunately there will be some negative factors in 2015 as well. They will be -1, -5, -13, -31, -65, -155, -403, and -2015.

Whatever life throws your way, I wish you a happy, healthy, and prosperous 2015.

### 336 and Level 2

• 336 is a composite number.
• Prime factorization: 336 = 2 x 2 x 2 x 2 x 3 x 7, which can be written 336 = (2^4) x 3 x 7
• The exponents in the prime factorization are 4, 1 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1)(1 + 1) = 5 x 2 x 2 = 20. Therefore 336 has exactly 20 factors.
• Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
• Factor pairs: 336 = 1 x 336, 2 x 168, 3 x 112, 4 x 84, 6 x 56, 7 x 48, 8 x 42, 12 x 28, 14 x 24 or 16 x 21
• Taking the factor pair with the largest square number factor, we get √336 = (√16)(√21) = 4√21 ≈ 18.330

These sixteen clues are all you need to complete this multiplication table!

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

### 335 and Level 1

• 335 is a composite number.
• Prime factorization: 335 = 5 x 67
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 335 has exactly 4 factors.
• Factors of 335: 1, 5, 67, 335
• Factor pairs: 335 = 1 x 335 or 5 x 67
• 335 has no square factors that allow its square root to be simplified. √335 ≈ 18.303

If you can multiply, divide and use a little logic, you should easily be able to complete this multiplication table puzzle.

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

### 334 and Level 6

• 334 is a composite number.
• Prime factorization: 334 = 2 x 167
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 334 has exactly 4 factors.
• Factors of 334: 1, 2, 167, 334
• Factor pairs: 334 = 1 x 334 or 2 x 167
• 334 has no square factors that allow its square root to be simplified. √334 ≈ 18.276

Is 1 or 2 the common factor for 6 and 8? Is 3 or 6 the common factor for 12 and 30? Is 4 or 8 the common factor for 40 and 16? In each case only one of those choices will make this puzzle work as a multiplication table? Can you figure out what those choices should be? Use logic to find the correct solution, not trial and error.

Print the puzzles or type the factors on this excel file:  10 Factors 2014-12-22

### 333 and Level 5

• 333 is a composite number.
• Prime factorization: 333 = 3 x 3 x 37, which can be written 333 = $3^2$ x 37
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 333 has exactly 6 factors.
• Factors of 333: 1, 3, 9, 37, 111, 333
• Factor pairs: 333 = 1 x 333, 3 x 111, or 9 x 37
• Taking the factor pair with the largest square number factor, we get √333 = (√9)(√37) = 3√37 ≈ 18.248

Print the puzzles or type the factors on this excel file:  10 Factors 2014-12-22

### 332 and a Christmas Star

• 332 is a composite number.
• Prime factorization: 332 = 2 x 2 x 83 which can be written $2^2$ x 83
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2 = 6. Therefore 332 has exactly 6 factors.
• Factors of 332: 1, 2, 4, 83, 166, 332
• Factor pairs: 332 = 1 x 332, 2 x 166, or 4 x 83
• Taking the factor pair with the largest square number factor, we get √332 = (√4)(√83) = 2√83 ≈ 18.221

Merry Christmas! This is a rather easy level 5 puzzle so I’m sharing it instead of a level 4 puzzle today.

Print the puzzles or type the factors on this excel file:  10 Factors 2014-12-22

Do You Hear What I Hear? by Noël Regney

Said the night wind to the little lamb,
Do you see what I see
Way up in the sky, little lamb,
Do you see what I see
A star, a star, dancing in the night
With a tail as big as a kite
With a tail as big as a kite

Said the little lamb to the shepherd boy,
Do you hear what I hear
Ringing through the sky, shepherd boy,
Do you hear what I hear
A song, a song, high above the trees
With a voice as big as the sea
With a voice as big as the sea

Said the shepherd boy to the mighty king,
Do you know what I know
In your palace warm, mighty king,
Do you know what I know
A Child, a Child shivers in the cold
Let us bring Him silver and gold
Let us bring Him silver and gold

Said the king to the people everywhere,
Listen to what I say
Pray for peace, people everywhere!
Listen to what I say
The Child, the Child, sleeping in the night
He will bring us goodness and light
He will bring us goodness and light