# 18 Up on the Housetop

18 is a composite number. 18 = 1 x 18, 2 x 9, or 3 x 6. Factors of 18: 1, 2, 3, 6, 9, 18. Prime factorization: 18 = 2 x 3 x 3, which can also be written 18 = 2 x 3².

When 18 is a clue in the FIND THE FACTORS puzzles, use either 2 x 9 or 3 x 6. Only one set of factors will work for any particular puzzle.

Up on the Housetop” is a famous children’s Christmas carol.  Imagine Santa stopping on each housetop to go down its chimney.

Up on the housetop – to solve these puzzles will require you to have knowledge of the multiplication facts and just a little imagination to see the housetops (and maybe the ability to tilt your head for most of them.) Place the numbers 1 – 10 in both the top row and the first column so that those numbers are the factors of the given clues. Click 10 Factors 2013-12-23 to print these puzzles or see last week’s solutions. In order to view the file, you need excel or other comparable spreadsheet program.

# 17 Christmas Angels

• 17 is a prime number.
• Prime factorization: 17 is prime.
• The exponent of prime number 17 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 17 has exactly 2 factors.
• Factors of 17: 1, 17
• Factor pairs: 17 = 1 x 17
• 17 has no square factors that allow its square root to be simplified. √17 ≈ 4.123.

How do we know that 17 is a prime number? If 17 were not a prime number, then it would be divisible by at least one prime number less than or equal to √17 ≈ 4.1. Since 17 cannot be divided evenly by 2 or 3, we know that 17 is a prime number.

17 is never a clue in the FIND THE FACTORS puzzles.

Many Christmas trees in the United States have been up and decorated for weeks. Some of them have a beautiful angel on the top to remind us of the angel that visited the shepherds. In Hungary, the angel is remembered in a different way. There the Christmas tree is put up on Christmas Eve. Tradition says that angels are the ones who decorate the tree with the delicious candies called szaloncukor. The candies are wrapped in specially prepared white tissue and fastened to the tree with white yarn. See the related articles at the end of the post for more information about this fascinating tradition.

The angel puzzles that I’ve made for this post have a few extra clues so they will be easier to solve. The first level 5 puzzle even has many of the same clues as the level 4 puzzle. Nevertheless, be careful because each level 5 angel has a few tricks up her sleeve. Still if you can write the numbers 1 to 12 in both the top row and the first column so that those numbers are the factors of the given clues, then you’ve solved the puzzle. There is only one solution to each puzzle. Click 12 Factors 2013-12-19 for a printable version of these and a few other puzzles.

Hungary:

United States:

# 14 Oh Christmas Tree

14 is a composite number. 14 = 1 x 14 or 2 x 7. Factors of 14: 1, 2, 7, 14. Prime factorization: 14 = 2 x 7.

When 14 is a clue in the FIND THE FACTORS  1 – 10 or 1 – 12 puzzles, use 2 and 7 as the factors.

O Christmas Tree, O Christmas Tree,

Do Christmas factor trees have lovely branches?  It depends on how they are constructed. For example here are 2 of the many possible factor trees for 1680. I think one of them is more lovely than the other.

This blog is actually about a logic puzzle that is based on the multiplication table. Today we have puzzles that look like Christmas trees, garland, lights, or blocks and a bright star for the very top.

Directions to solve the puzzles: In both the top row and the first column place the numbers 1 – 10 so that they are factors of the given clues. It may be more challenging than you think, especially for the higher level puzzles. If you click 10 Factors 2013-12-09, you can print the puzzles in color or black and white from an excel spreadsheet or you can type the answers directly on the spreadsheet. You must have a spreadsheet program on your device to access the file.

# 13 Mikulás

• 13 is a prime number.
• Prime factorization: 13 is prime.
• The exponent of prime number 13 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 13 has exactly 2 factors.
• Factors of 13: 1, 13
• Factor pairs: 13 = 1 x 13
• 13 has no square factors that allow its square root to be simplified. √13 ≈ 3.60555.

How do we know that 13 is a prime number? If 13 were not a prime number, then it would be divisible by at least one prime number less than or equal to √13 ≈ 3.6. Since 13 cannot be divided evenly by 2 or 3, we know that 13 is a prime number.

13 is never a factor in the FIND THE FACTOR 1 – 10 or 1 – 12 puzzles.

Tonight (December 5th) all over Hungary, children will polish their boots and then place them in a window or in front of their door. Once the children are “nestled, all snug in their beds, … visions of sugar-plums (will indeed) dance in their heads” as they await a visit from Mikulás, or St. Nickolas.  When the children get up in the morning, they will find their boots or shoes filled with candy, fruit, and nuts if they have been good. If they have been bad, their boots or shoes will be filled with virgács, a small collection of twigs that have been spray-painted gold and decoratively bound together.

Since most children were good some of the time and naughty once in awhile, they will likely find  the expected goodies as well as virgács in their shoes or boots.
With these traditions in mind, I created the puzzles for today. If you have just a little imagination, you will be able to see different types of candy as well as the virgács in the clues. These puzzles will be a treat to any child or adult who did their homework and learned multiplication, division, and factoring. Click 12 Factors 2013-12-05.