# 1676 Really, How Well Can You Read a Table?

### Today’s Puzzle:

Reading a table is an important mathematical skill. Can you read names from a table even if the table is written in a different language? Note: in Hungary, the surnames are written before the given names.

Debreczeni Eszter was born on 23 February 1855. I know this because that was the date written by the minister on her church’s marriage index.

Today’s puzzle: Look at this table of baptisms and determine the names of Debreczeni Eszter’s parents.

If like me, you quickly determined from entry 79 that Debreczeni Eszter was indeed born on February 23 and baptized on March 28, and her parents’ names were Debreczeni János and Rácz Erzsébet, you will feel quite confused when you look at her 1876 marriage record:

Her father’s name was Debreceni Sándor? What? The birth year of 1855 would be right for a 20-year-old marrying in January of 1876, but when I looked for her on FamilySearch, I didn’t find anyone with her name with that father’s name. Did she lie about her age when she married? Did the minister get it wrong on either the marriage record or the marriage index? She was a member of the Reformed Church when she married, but perhaps she was Lutheran or Jewish when she was born? (Those records haven’t been indexed yet.)

I looked at the marriage index again.

You can see their entry on the top by the date jan. 5. As you can see, the minister did not write in dates of birth for all those getting married. Did he get this 1855-ii-23 birthdate wrong?

Knowing that if she lived into the 20th century, there was a good chance the names of her husband as well as both of her parents would appear on her death record, I looked through years of not-yet-indexed death records, and I finally this Debreczeni Eszter record that gives a quick snapshot of her life!

She died 1913 Oct 31 at 2:00. Her name Finta Andrásné (Mrs. András Finta), Debreczeni Eszter. She was 58 years old (born about 1855) when she died. Her husband was Finta András and her parents were the late Debreczeni Sándor and the late N. Nagy Eszter.

I was still puzzled. Searching for Debreczeni Eszter in 1855 through FamilySearch brought up only the Eszter that was a daughter of János and another Eszter, the daughter of Imre. The table of Túrkeve Reformed Church 1855 christenings was 52 pages long and had 324 entries. Perhaps her entry had been indexed incorrectly. I searched again using only first names and found a possible candidate, Nagy Eszter, who was baptized on March 1. I looked at the 1855 baptismal record again. And then I saw it. The minister didn’t get it wrong, the bride didn’t lie about her age: I needed to read the table better! It turns out two baby girls named Debreczeni Eszter were born on February 23rd, but I hadn’t looked past the first one listed. Look at the last entry in the table below. It is the christening record I was looking for!

Eszter, entry number 33, was born on 23 February and baptized on 1 March. Her parents were listed as Debr. Nagy Sándor and Nosza Nagy Eszter. (Having more than one surname was common in Hungary.) When this baptism was indexed by FamilySearch, the parents were understandably indexed as Nagy Sándor and Nagy Eszter, which also let them hide from me easier.

How did you do with this puzzle? You may have been faster than I was, but I knew something was wrong with my findings, and I stuck with it until I figured it out. Those are also important mathematical skills!

### Factors of 1676:

Since this is my 1676th post, I’ll write a little about the number 1676.

1676 happens to be 200 years before the marriage I wrote about above.

• 1676 is a composite number.
• Prime factorization: 1676 = 2 × 2 × 419, which can be written 1676 = 2² × 419.
• 1676 has at least one exponent greater than 1 in its prime factorization so √1676 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1676 = (√4)(√419) = 2√419.
• 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 1676 has exactly 6 factors.
• The factors of 1676 are outlined with their factor pair partners in the graphic below.

### More About the Number 1676:

From OEIS.org, we learn that 1676 = 1¹ + 6²  + 7³ + 6 .

1676 is the difference of two squares:
420² – 418² = 1676.

# How Are These Two DNA Shared Matches Related to Each Other?

My husband shares 20 cM across 2 segments with one of his DNA matches. I wanted to figure out their relationship because the surname Ungi from the match’s pedigree chart was familiar to me. I had seen it on family records originating in Gyoma, Hungary where my husband’s paternal grandparents were born.

I was also curious because this 20 cM-match was a shared match with someone else, a 143 cM-match that I found several years ago – without using DNA.

I started with the 20cM-match’s pedigree chart. There was a great-grandmother (Ungi Juliánna) who died 7 March 1950 in Hahót, Hungary and had been born 29 years earlier (about 1921) in Gyoma. Eventually, I was able to make this diagram showing the relationship between my husband’s two matches.

I didn’t make a separate chart, but my husband and his 143 cM match are 2nd cousins once removed.

Here are the supporting documents I used to make the chart. (You will need to be signed into a free FamilySearch account to see these records) Names on the chart are in bold:

Hahót, Zala civil registration death record line 12, Ungi Juliánna, died 7 March 1950, age 29, from drowning. Her husband was Domján István. Her parents were Ungi Zsigmond and Kéri Mária.

Gyoma Marriage Civil Registration, Page 102, Date 10 December 1898, Groom Ungi Zsigmond, born 16 August 1874, the son of the late Ungi Lajos and Kéri Juliánna. Bride Kéri Mária, born 25 March 1879, the daughter of Kéri István and Szalóki Zsuzsánna.

Christening dates of Kéri István and Szalóki Zsuzsánna’s children
30 Mar 1879 Mária
29 Sep 1881 Susánna (Zsuzsánna)
03 Jul 1885 István
18 Jan 1890 János (died 26 Feb 1890)
That’s all the documents I needed to show how they were related to each other, but how is my husband related? Here is a chart showing how he is related to the 20 cM match:
I found some other family records that may interest you:
Marriages and Children of Juhász Erszébet
23 October 1839 The Reformed Church marriage record states that Szűts György’s son Mihaly, age 37, a widower, weds Juhász Janos’s daughter Ersébet, age 21. He was born about 1802; she was born about 1818
02 Aug 1841 son Szűcs Mihály

19 Oct 1852 son István Line 306, parent Rác Mihály’s widow, Juhász Erzsébet. Note in margin states that István got permission to change his surname from Juhász to Kéri, the surname of his stepfather Kéri Mihály
14 September 1853 marriage record to the widower Kéri Mihály states that she was the late R. Szűcs Mihály’s widow. It should be noted that Kéri Mihály’s wife of nearly 24 years died just a few weeks earlier on 10 August 1853 during childbirth. You can read more about Kéri Mihály in my posts, 550 Godparents and 543 Arithmetic and Genealogy.
23 Sep 1854 daughter Kéri Lidia

Some of the information above I found a few years ago, but finding new tidbits of information about a cousin or ancestor is so exciting. I hope you can discover the thrill yourself!

# 1370 Detail Left Out of the History Books

Today I was indexing some July 1944 death records from Budapest, Hungary and noticed that Boldizsár Klein and his wife, Regina Leichtmann, died only one day apart from each other. We don’t index causes of death, but I looked at their causes of death because their deaths were so close to each other. The same word was used for both causes of death. I wasn’t sure of all the letters in the word, but it started the same as a word I had seen before, öngyilkos, which literally means self-murder.

First I consulted my hardback Hungarian dictionary, but I didn’t find the word. Next, I looked at two online Hungarian genealogy dictionaries. Finally, I typed what the letters most looked like to me into Google Translate. After a few trials and errors with different letters of the alphabet with and without the prefix, ön, I found the word and their cause of death, önmérgezés, which means self-poisoning or intoxication.

Why did this happen to them?!!

From the record, I knew that both 74-year-old Boldizsár and 66-year-old Regina were Jewish. I googled and learned that the Nazis invaded its previous ally, Hungary, only a few months earlier on 19 March 1944 and mass evacuation of Jews to death camps began immediately. Since this couple lived in Budapest, the horrors of this occupation must have been felt most intensely. I cannot imagine what they went through, but trying to put ourselves in their shoes may help prevent history from repeating itself.

This is my 1370th post, so I’ll write a little bit about that number:

• 1370 is a composite number.
• Prime factorization: 1370 = 2 × 5 × 137
• 1370 has no exponents greater than 1 in its prime factorization, so √1370 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 1370 has exactly 8 factors.
• The factors of 1370 are outlined with their factor pair partners in the graphic below.

1370 is the hypotenuse of four Pythagorean triples:
74-1368-1370 which is 2 times (37-684-685)
312-1334-1370 which is 2 times (156-667-685)
822-1096-1370 which is (3-4-5) times 274
880-1050-1370 which is 10 times (88-105-137)

OEIS.org informs us that 1² + 37² + 0² = 1370.

# 1178 School Supplies

There is so much to see at the Ópusztaszer National Heritage Park whose location marks the birthplace of the nation of Hungary. I will mention only two of its attractions in this post.

In the rotunda is a huge cyclorama painting by Arpad Feszty depicting the arrival of the Magyars over 1100 years ago. The painting in of itself is amazing, but it is also augmented with artificial landscapes in front of and all the way around the painting, giving it a 3D effect. Photography in the rotunda is forbidden, but there is no way to capture the magnificence of this work of art in a 2-dimensional photo anyway. (Neither do these few words I’ve written.)

The 15-building museum village includes a school. I was pleased to see some of the authentic school supplies from around the turn of the 20th century and before. This first one is a slate students could use not only to write mathematical calculations but also to graph equations or make bar graphs!

This abacus also made me smile.

I would encourage you to visit Ópusztaszer National Heritage Park should you get to visit Hungary, but give yourselves more than the two hours we did to enjoy all it has to offer.

Now I’ll share some information about the number 1178:

• 1178 is a composite number.
• Prime factorization: 1178 = 2 × 19 × 31
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1178 has exactly 8 factors.
• Factors of 1178: 1, 2, 19, 31, 38, 62, 589, 1178
• Factor pairs: 1178 = 1 × 1178, 2 × 589, 19 × 62, or 31 × 38
• 1178 has no square factors that allow its square root to be simplified. √1178 ≈ 34.322

1178 is a leg in a few Pythagorean triples including
600-1178-1322 calculated from  31² – 19², 2(31)(19), 31² + 19²

1178 is palindrome 212 in BASE 24 because 2(24²) + 1(24) + 2(1) = 1178

# 862 Look What a Little Bit of Spit Can Tell You!

All four of my husband’s grandparents were born in Hungary.

Recently my husband ordered a DNA kit from ancestry.com. When the kit arrived, he spit into the kit’s tube until his spit reached the indicated line and mailed it back to Ancestry. This week he received his results, and I was thrilled!

I made the map below based on Ancestry’s map of his genetic communities as well as other maps showing what Hungary looked like in the 1800’s. Near the center of the map, we see a rough outline of what Hungary looks like today. When his grandparents were born, Hungary was three times bigger than it is today so I’ve made an outline to show the size of the country that they knew and loved.

Places, where there is DNA similar to that of my husband, are shown in pink. The three red dots indicate the known locations of my husband’s grandparents’ births. The town names are in big bold red letters even though they were all little villages or small towns. Gyoma used to be in the center of Hungary. Now it is very close to the Romanian border. Zádorfalva is barely in the country while Szürte is barely outside. I didn’t indicate it on the map but my husband’s father was born in a little village southeast of Gyoma. It was part of Hungary when he was born but part of Romania now.

This map is not necessarily about where my husband’s grandparents were born, however. This map also shows where some of THEIR ancestors lived hundreds of years ago. Even though TWO of his grandparents were born in Gyoma, the map seems to indicate that their ancestors moved to Gyoma from someplace else. Also, if my husband’s brother took a DNA test, his map would look a little different because a child receives only half of each parent’s DNA, and the half received can vary from child to child.

My husband’s paternal grandfather, István Sallai, was born in Gyoma, as were his parents and grandparents for several generations. Our research goes back to the 1770’s where all of his ancestors were either born in Gyoma or else they moved to Gyoma from Túrkeve, a town 34.8 km to the north. Sallai means “from Salla”, but we are not certain where Salla might have been. Maps give many possibilities. Also, Frank Kery is one of my husband’s second cousins through this line, and he made the list of potential 2nd and 3rd cousins that the DNA test gave. That helps confirm our faith in the accuracy of the test.

István’s wife, Mária Finta, was also born in Gyoma, as were many generations of her family on her father’s side. Her 2nd great-grandfather, Mihály Finta moved to Gyoma from Túrkéve where MANY people with the surname Finta have lived over the years. On the other hand, Mária’s mother was of Slovak ancestry and was born in Szarvas which is 24.4 km to the west of Gyoma. The Lutheran Church in Szarvas kept wonderful records so I was able to find most of her ancestors back to the mid 1700’s. Sometime around or soon after 1720, her Slovak ancestors moved to Szarvas from whatever Slovak town in which they used to reside.

My husband’s maternal grandfather was born in Szürte, Ung county, Hungary which is now part of Ukraine. We do not have access to any records in the area so other than the names of his parents and possibly some siblings, we know very little about his family. This map and ancestry.com’s DNA database will likely match and introduce us to cousins my husband never knew he had.

Zádorfalva is located where most of the pink is concentrated on the map. My husband’s maternal grandmother, Erzsébet Lenkey was born in Zádorfalva. Both of her parents were born to noble families so we have the names of many of her ancestors back as far as the 1200’s for some lines who also lived there. Zádorfalva is still in Hungary near the Slovakian border. The other towns of her ancestry are close-by in what used to be Gömör county, Hungary. Now those towns are on one side or the other of the Hungary-Slovakian border. The Hungarian names for these towns include Alsószuha, Mihályfalva, Horka, and Kövecses. The noble families of these small towns tended to stay in town generation after generation, leaving only if they married into another noble family and relocated to that family’s town. It makes perfect sense to us that this part of the map has the greatest concentration of pink.

I am certain that if you took a DNA test, you would delight in the information given, too! You might also enjoy reading Ancestry.com’s research about DNA and western migration in North America.

Since this is my 862nd post, I’ll now write a little bit about the number 862:

I learned from OEIS.org that the sum of the factors of 862 is not only a perfect square but also a perfect fourth power:

1 + 2 + 431 + 862 = 1296 = 36² = 6⁴.

• 862 is a composite number.
• Prime factorization: 862 = 2 × 431
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 862 has exactly 4 factors.
• Factors of 862: 1, 2, 431, 862
• Factor pairs: 862 = 1 × 862 or 2 × 431
• 862 has no square factors that allow its square root to be simplified. √862 ≈ 29.3598

# 550 Godparents

All of these children are more puzzle pieces in the life of Kéri Mihály (Michael Keri).

I’m sharing this chart even though I have not yet found all of the children’s death dates. The highlighted entries will help me explain a thing or two.

The parents listed for the Sára christened in 1842 are Kéri Mihály and Cselei Rebeka (highlighted in blue). I believe the minister made a mistake writing Cselei instead of Nyilas. Here are my reasons:

1. I didn’t find a Kéri-Cselei marriage record or any other children for a couple with those names.
2. Kéri Mihály and Nyilas Rebeka had a child every two to three years. There would be a five year gap if 1842 Sára is not included in the family.
3. The couple had a previous child they named Sára who died in 1841, a year before 1842 Sára was born.
4. 1842 Sára’s godparents were also the godparents of five of her siblings. I looked to see if Michael Keri and Rebeka were the godparents for the Sandor Josik and Rebeka Horvat’s children. They weren’t, but Sandor Josik and Rebeka Horvat also were not the godparents for any other couple from 1841 to 1843.

Another mistake was obviously made recording dates for Ester who has some conflicting dates highlighted in red. I double checked all the information when I added it to the chart. If you were to follow the christening record and the death record, Ester was born on the 7th, christened on the 7th, died on the 6th, and buried on the 8th. Her death record also stated that she was 3 days old when she died. Obviously at least one of the dates is not correct.

Life must have been very difficult for Michael and Rebeka Keri. A little baby usually represents much hope for the future. This couple had to witness the deaths of too many of their little ones. My heart goes out to them.

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550 is the product of 10 and the 10th triangular number and is, therefore, the 10th pentagonal pyramidal number.

550 is the hypotenuse of two Pythagorean triples: 330-440-550 and 154-528-550. What is the greatest common factor of each of those triples?

• 550 is a composite number.
• Prime factorization: 550 = 2 x 5 x 5 x 11, which can be written 550 = 2 x (5^2) x 11
• The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 550 has exactly 12 factors.
• Factors of 550: 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550
• Factor pairs: 550 = 1 x 550, 2 x 275, 5 x 110, 10 x 55, 11 x 50, or 22 x 25
• Taking the factor pair with the largest square number factor, we get √550 = (√25)(√22) = 5√22 ≈ 23.452079

# 487 The Forgon Family Tree

Before I write about the Forgon Family, I’ll write just a little bit about the number 487 beginning with something I learned from Number Gossip:

• 487¹ = 487, and 4 + 8 + 7 = 19.
• 487³ = 115,501,303, and 1 + 1 + 5 + 5 + 0 + 1 + 3 + 0 + 3 = 19.

It’s pretty cool that both sums equal each other, but it’s even cooler that 487 is the smallest prime number that can make that claim.

487 = 157 + 163 + 167, so 487 is also the sum of three consecutive prime numbers.

• 487 is a prime number.
• Prime factorization: 487 is prime.
• The exponent of prime number 487 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 487 has exactly 2 factors.
• Factors of 487: 1, 487
• Factor pairs: 487 = 1 x 487
• 487 has no square factors that allow its square root to be simplified. √487 ≈ 22.068076

How do we know that 487 is a prime number? If 487 were not a prime number, then it would be divisible by at least one prime number less than or equal to √487 ≈ 22.068. Since 487 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 487 is a prime number.

—————————————————

Andor Forgon and my son, David. Andor is the caretaker of the Mihály Forgon museum in Mihályfalva. David wrote, “Andor Forgon, who is a distant cousin (If I’ve done my math right we’re tenth cousins twice removed. You’d have to go back to the 1600s to find a common ancestor). Still, he had a lot of interesting information about the Forgon branch of our family and about the history of Mihályfalva.”

My husband’s second great-grandmother was named Erzsébet Forgon. She was born into Hungarian nobility in a little village called Mihályfalva in what is now southern Slovakia. Her parents were Juditha Dancs and Boldizsár Forgon.

Since Erzsébet was born into a Catholic family, we were not able to find her christening record in Mihályfalva. It was very discouraging pouring over the Reformed Church records, seeing plenty of people with the name Forgon, but not her christening record. I found the record of her conversion from Catholicism to the Reformed Church. It’s the last record on the page below. The images are small, but if you click on them, you should be able to read them much more easily.

I was also able to find her marriage record. It is the first entry in the year 1856.

I had almost given up hope finding her christening record. When my son and I visited Mihályfalva three years ago, he asked someone in town where a Catholic would take their children to get baptized. The town named seemed so far away. We looked online a little but did not immediately find her christening record.

Because Familysearch volunteers have indexed so many records, we were able to find Erzsébet’s 9 October 1836 christening record here. Her christening is listed near the top of the second of the two pages of the document.

I was also able to find the 5 June 1809 christening record of her father, Boldizsár son of János Forgon and Krisztina Nagy.  That baptism is the second entry in June, and his brother’s christening is listed right under his.

The 8 May 1768 christening of my husband’s 4th great grandfather, János Forgon, son of Péter Forgon and Borbála Kovács is the third entry on the first page of this document.

This 19 June 1741 document appears be the christening record of my husband’s 5th great grandfather Péter Forgon, son of István (Stephan) Forgon. It is the 7th entry on the 2nd page of the document. This christening occurred in Mihályfalva at a time when mothers were not considered important enough to list on records. Péter and his brother István who was christened 26 April 1743 (1st page; 17 entry) both converted to Catholicism.

All of these ancestors lived in Mihályfalva and the Catholic baptisms were performed in two different towns. I probably would not have found any of them if they had not been indexed and if not for the genealogical work done by one of my husband’s most important relatives. A very short account of his life follows:

One of the most famous people named Forgon was Dr. Mihály Forgon. His 22 October 1885 christening is 4th from the bottom of the first page. While he worked on his law degree he found time to compile descendant charts for the many noble families who lived in Gömör County, Hungary. After receiving his law degree, Dr. Forgon worked as a prosecutor. During World War I, he served as a reserve lieutenant on the Russian front in Poland.  About three weeks after he arrived in Poland, he was tragically and fatally shot. He was only 29 years old.

I’ve included the descendant table Mihály Forgon made for the Forgon family below. After not too many years a descendant chart becomes much too large to fit on one single sheet of paper so Mihály Forgon separated the descendant chart into three additonal tables. The earliest date on the main table is 1573, and it maps the way to the remaining tables as follows:

• Four generations below Forgon János we have Balint who becomes the top of table #IV. (We will see my husband’s family on this table.)
• The next generation has János who becomes the top of table #III.
• That same generation also has Zsigmond, the father of István and Zsigmond who are at the top of table #II.

Dr. Mihály Forgon name is listed near the bottom of table #I under the names of his parents, Rafáel Forgon and Erzsébet Bodon. Forgon and Bodon were both noble families and the most honored surnames in Mihályfalva.

My husband’s second great grandmother, Erzsébet, is listed on this fourth chart. You can see her name in the middle of the chart approaching the right hand side under Boldizsár and his wife Juditha Dancs. Erzsébet’s husband, Ferdinánd Barna, is listed just below her name.

One of the reasons I wanted to write about the Forgon family is because I’ve met one of its members on WordPress. The beautiful Veronika Forgon also traces her roots back to Mihályfalva to this noble family. She is the lovely model featured in these four posts:

Veronika Forgon – Hajógyári Sziget

Veronika Forgon – Buda Castle

Veronika Forgon – Margitsziget

Veronika Forgon – Kopaszi Dam

Update: When I wrote this post I wasn’t exactly sure how Veronika is related to my husband and my children, but after reading it, she contacted us, and now I know! I was thrilled to learn that she is my husband’s 11th cousin, and my children are her 11th cousins once removed.

# 73 and Once

In Hungarian, “Multiplication Table” and “Times Table” are the same expression as “Once Upon a Time”. I very much enjoyed learning that when I went to the school of fairies today where even butterflies can learn to multiply. The author translates a sweet poem from Hungarian into English. I hope you will read the poem and remember its encouraging words whenever you try to solve one of my multiplication table puzzles or any other task that challenges you in life.

• 73 is a prime number.
• Prime factorization: 73 is prime.
• The exponent of prime number 73 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 73 has exactly 2 factors.
• Factors of 73: 1, 73
• Factor pairs: 73 = 1 x 73
• 73 has no square factors that allow its square root to be simplified. √73 ≈ 8.5440037

How do we know that 73 is a prime number? If 73 were not a prime number, then it would be divisible by at least one prime number less than or equal to √73 ≈ 8.5. Since 73 cannot be divided evenly by 2, 3, 5, or 7, we know that 73 is a prime number.

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

73 is included in this list of prime numbers:

# 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:

# 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.