# 1722 Mikulás, Fill My Boot With Goodies!

Contents

### Today’s Puzzle:

Today is December 5, so children in Hungary and some other countries will shine their boots and put them out for Mikulás (Saint Nick) to fill with candies. Can you solve this boot puzzle? Write the numbers 1 to 10 in both the first column and the top row so that the given clues are the products of the numbers you write.

Here is a song children will sing in Hungary today. You are already familiar with the tune. This particular video includes subtitles.

Here are the lyrics in Hungarian and Google’s translation into English:

Hull a pelyhes fehér hó, jöjj el kedves Télapó!
Minden gyermek várva vár, vidám ének hangja száll.
Van zsákodban minden jó, piros alma, mogyoró,
Jöjj el hozzánk, várunk rád, kedves öreg Télapó.

Nagy szakállú Télapó jó gyermek barátja.
Cukrot,diót, mogyorót rejteget a zsákja.
Amerre jár reggelig kis cipőcske megtelik,
megtölti a Télapó, ha üresen látja!

The fluffy white snow is falling, come dear Santa!
Every child waits expectantly, the sound of happy singing is heard.
You have everything good in your bag, red apples, hazelnuts,
Come to us, we are waiting for you, dear old Santa Claus.

Santa Claus with a big beard is a good friend of children.
His sack hides sugar, walnuts and hazelnuts.
Wherever you go, your little shoe will be full by morning,
Santa will fill it if he sees it empty!

### Factors of 1722:

• 1722 is a composite number.
• Prime factorization: 1722 = 2 × 3 × 7 × 41.
• 1722 has no exponents greater than 1 in its prime factorization, so √1722 cannot be simplified.
• The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1722 has exactly 16 factors.
• The factors of 1722 are outlined with their factor pair partners in the graphic below.

### More About the Number 1722:

Since 1722 = 41·42, we know that 1722 is the sum of the first 41 EVEN numbers. It is two times the 41st triangular number.

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