A Multiplication Based Logic Puzzle

Archive for the ‘My Family’ Category

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

All four of my husband’s grandparents were born in Hungary. Back then Hungary was three times the size that it is now.

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! This map of his genetic communities was part of his report. My son, David, added three red dots to show the known locations of my husband’s grandparents’ births.

This map is not necessarily about where his grandparents were born, however. This map 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. The map gives 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 data base will likely match and introduce us to cousins he never knew he had.

Zádorfalva is located where most of the yellow 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 yellow.

I am certain that if you took a DNA test, you would delight in the information given, too!

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

I learned from Stetson.edu 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


861 Interpolating Genealogical Data

Not that long ago, calculators were expensive and bulky. Algebra students did calculations using lots of different tables: trig tables, square root tables, logarithm tables. Students could quickly multiply or divide two decimals by adding or subtracting their logarithms and then taking the antilogarithm of the sum or difference. Each table was only a few pages and was found in the back of the Algebra or Trig textbook. These small tables contained information for thousands of numbers. Interpolating information in the tables was a skill that was taught and learned. What is interpolation? Interpolation is an estimate of a value that falls between two other values. You could say that interpolating means the same thing as reading in between the lines.

People who research their genealogy interpolate; they read between the lines. Doing so helps answer questions like this:

Some people live on this earth only for a few minutes, others for 70 years or more. If a septuagenarian kept a diary of his life, it could consist of hundreds of pages and be a rich resource of how that person lived. Most people don’t journal their lives, however. All that may still exist from a person’s life is a few dates scattered in various record books. Nevertheless, finding those dates and piecing together an ancestor’s life can feel so rewarding. Interpolating some of the data found often helps make that person come alive to the researcher.

As I’ve researched my husband’s family, I’ve a particular couple’s name over and over again. The wife’s maiden name was Bíró, the same as her husband’s surname, and that was the same surname as one of my husband’s great-great grandmothers. I wondered if either one of them was related to her. Over time I found the answer to that question and in the process learned a bit about the two of them, and I’d like to share some of that here.

How Eszter became Bálint Bíró’s second wife:  Bálint’s father, Mihály, died when he was only 9 years old.  From the time that he was 12 years old when his older brother married, Bálint was the oldest son living at home.  Five days before his 31st birthday, Bálint married Erzsébet Szilágyi. A year and a half later, she gave birth to László Bíró on 28 Feb 1859.  He was christened five days later.

At this time, Bálint’s mother, Susánna Nagy Bíró, was 67 years old and suffered from feebleness and weakness.  She died on 9 May 1859 when her brand new grandson was just 2 months old.

The next day Bálint’s wife died from a stroke.  She was only 21 years old! The responsibility of caring for her baby boy AND her feeble mother-in-law must have been all hers. What stress she must have felt! It literally killed her. Bálint went to his mother’s funeral on the 10th and to his wife’s funeral on the 11th of May. I can’t imagine his grief.

It was not at all unusual for a young father in Hungary to remarry soon if his wife died. So after two weeks of mourning and courtship, Bálint found a mother for his infant son.  He and Eszter announced their engagement on 26 June that same year.  When they married on 10 July 1859 in the Reformed Church in Gyoma, Békés, Hungary, he told her and the preacher that he was 10 years older than she was.  He was actually 16 years older.  Here is a list of their children. Several of them lived very short lives.

As you read the dates in that table, do you find yourself interpolating the feelings they might have had? Can you not help but to read in between the lines? How did it feel to take care of small children suffering with scarlet fever and then seeing them succumb to the disease?

There is almost an eleven year gap between the births of their children, Bálint and Benedek. Coincidentally, there was another couple in town having children during this time who had similar names, Benedek Bíró and Eszter Bíró. It was important not to get them confused with our Bálint Bíró and Eszter Bíró. They lived in a completely different houses and were not the same people!

Bálint and Eszter Bíró were well liked in their community, and they took their religious duties very seriously.  On several occasions when a couple in the town were married, Bálint was recorded as one of the two witnesses.  Many parents asked the two of them to be their children’s godparents. In fact, Dániel Finta, who was my husband’s great-grandfather and Bálint’s nephew, requested that Bálint and Eszter be the godparents to his firstborn son, Dániel.

What do their names mean?

Bálint is the Hungarian form of Valentinus which means “healthy or strong”. Bálint would have celebrated his name day each February 14th.

Eszter comes from the Hebrew word for “star”.  Queen Esther is a courageous woman in the Bible who saved thousands of her people. Eszter would have celebrated her name day each May 24th, which was the day after her birthday.

Bíró is the Hungarian word for “judge”.

What I know about Eszter Bíró’s early life:  Eszter was born 23 May 1842 to Benedek Bíró and Mária Ladányi.  Here is a table that contains Eszter and her siblings:

Almost half of Eszter’s ten siblings died before she was born. After losing so many of their precious children, her parents must have cherished her. She was their oldest surviving daughter.

Eszter’s paternal grandmother was Sára Kurutsó. Kurutsó was one of the three noble surnames in Gyoma, Békés, Hungary. Over the next century that surname changed into Krutsó, Krucsó, or Kruchió.  Noble families weren’t necessarily richer than their neighbors, but they had a title! Eszter was probably aware of her grandmother’s status.

Eszter completed her religious confirmation classes on 16 March 1856, a few weeks before her 14th birthday. In Hungary, birthdays were not necessarily celebrated as much as name days were, however.

What I know about Bálint Bíró’s early life: Bálint was born 18 Nov 1826 to Mihály Bíró and Susánna Nagy. Here is a table listing Bálint and his siblings. His sister, Sára Bíró, who was 3½ years his senior, is my husband’s great-great grandmother.

As you can see there are some blank spots in the table because I haven’t found all the information about this family yet.

I have found a little information about the number 861, and since this is my 861st post, I’ll share that here:

From Stetson.edu I learned that 7 + 77 + 777 = 861. Since that is six 7’s, 861 has to be divisible by 3, but not by 9. (It would have to have nine 7’s to be divisible by nine.)

861 is the hypotenuse of a Pythagorean triple: 189-840-861, which is 21 times (9-40-41).

861 is the 41st triangular number because (41 × 42)/2 = 861. That means that 1 + 2 + 3 + . . . + 39 + 40 + 41 = 861.

861 is also the 21st hexagonal number because 2(21²) – 21 = 861. (All hexagonal numbers are also triangular numbers.) That means that 1 + 5  + 9 + 13 + 17 + 21 + 25 + . . . + 73 + 77 + 81 = 861.

  • 861 is a composite number.
  • Prime factorization: 861 = 3 × 7 × 41
  • 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 861 has exactly 8 factors.
  • Factors of 861: 1, 3, 7, 21, 41, 123, 287, 861
  • Factor pairs: 861 = 1 × 861, 3 × 287, 7 × 123, or 21 × 41
  • 861 has no square factors that allow its square root to be simplified. √861 ≈ 29.3428.

571 Family Time

For the last two weeks we’ve been spending time with our grandchildren in Salt Lake City, Utah; Portland, Oregon; Houston, Texas; and Hartford, Connecticut. We also spent time with my brother’s daughter and her two children. AND we celebrated my sister’s 70th birthday party and reconnected with all of her children in Portland. We have been busy, and I am tired, but happy.

We’ve had a wonderful time with all of them, and it was so painful to say goodbye. We and a few other people took pictures except we didn’t get any pictures of the grandkids that live within 10 miles of our home. What’s with that? I’m as guilty as anyone else who takes people and things for granted.

Here’s a picture of me holding my newest grandson. My daughter is in the background holding one of her nieces.



Since 171 + 190 + 210 = 571, it is the sum of the 18th, 19th, and 20th triangular numbers. That makes 571 the 20th centered triangular number.

  • 571 is a prime number and a twin prime with 569.
  • Prime factorization: 571 is prime.
  • The exponent of prime number 571 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 571 has exactly 2 factors.
  • Factors of 571: 1, 571
  • Factor pairs: 571 = 1 x 571
  • 571 has no square factors that allow its square root to be simplified. √571 ≈ 23.8956

How do we know that 571 is a prime number? If 571 were not a prime number, then it would be divisible by at least one prime number less than or equal to √571 ≈ 23.9. Since 571 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, or 23, we know that 571 is a prime number.



557 Hungarian Genealogy Dictionaries

For many years I’ve used this Hungarian Genealogy Word List from FamilySearch to assist me as I’ve researched my family’s Hungarian genealogy.

This week I found another online Hungarian-English Dictionary. I really like this particular one because for each letter of the alphabet it gives a separate list of diseases beginning with that letter. Knowing the names of diseases in Hungarian is very helpful when looking looking at death records because often the cause of death is listed on the record.

If you are interested in word lists for some other language, you should be able to find it at FamilySearch.org.

Between those two word lists and an old Hungarian-English dictionary a genealogist friend gave me, I can find the meaning of most words I see. Sometimes I still have to ask my son who speaks Hungarian fluently for assistance, and sometimes the handwriting is so bad that even he can’t read it, but for the most part we are able to read and understand the records.

FamilySearch included a chart to help people recognize the names of Hungarian months found in the records. When I looked at our family’s records, I sometimes found month names that were not included on their chart, so I expanded the table to include some of these other names, too. The chart is not very difficult to read: the first column is in English, and the last column is in modern Hungarian and looks quite similar to English.

Hungarian Months

557 is the sum of two squares: 557 = 14² + 19²

557 is the hypotenuse of the primitive Pythagorean triple 165-532-557.

  • 557 is a prime number.
  • Prime factorization: 557 is prime.
  • The exponent of prime number 557 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 557 has exactly 2 factors.
  • Factors of 557: 1, 557
  • Factor pairs: 557 = 1 x 557
  • 557 has no square factors that allow its square root to be simplified. √557 ≈ 23.6008

How do we know that 557 is a prime number? If 557 were not a prime number, then it would be divisible by at least one prime number less than or equal to √557 ≈ 23.6. Since 557 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, or 23, we know that 557 is a prime number.

550 Godparents

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

Kéri Mihály's children


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.


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

543 Arithmetic and Genealogy

Doing genealogy is like working on a puzzle. Sometimes the smallest detail can be so important when determining who a person is. Sometimes doing a little adding or subtracting can be very helpful, too.

543-Subtracting dates


Unfortunately in the 1800’s many people were illiterate, and their arithmetic skills were sometimes lacking even more than that of people today. The ages given at marriage are not always accurate perhaps because the people didn’t know their true age or possibly because they added or subtracted a few years to appear older or younger than they really were. Sometimes the ages given at death are a little more accurate.

In the town of Gyoma in Békés County, Hungary there were several men named Kéri Mihály (Michael Keri). One of them was a widower who married a widow named Juhász Erzsébet (Elizabeth Juhasz or Elizabeth Shephard) on 14 September 1853 in the Hungarian Reformed Church in town. Their marriage record stated that he was 48 years old when they married, and the bride was 34.

I wanted to know exactly who this particular Michael Keri was. I looked through the Reformed Church records to find out more about him. I decided to look for his death record hoping that it would list his wife’s name on the record to help identify him.

I already knew that one year and six days after their wedding, the couple’s only child was born, a daughter that they named Lidia. Since her christening record indicated that her father was still living when she was baptized, I looked at death records beginning the very next day. After searching through over 15 years of records, I found two death records of men named Michael Keri. Unfortunately neither record mentioned a spouse or any other pertinent information. Were either of these men the person I sought?

I kept looking until I found his wife’s death record. Her record had much more information on it. It said that she was the wife of the late Keri Mihály so I knew for sure that one of those two men was her husband, but which one?

Since HER death record said how long she had been married and how long she had been widowed, I put that information at the bottom of the following chart next to her name, Juhász Erzsébet. I also did a little arithmetic to try to determine which Kéri Mihály best fit the numbers on her death record and put their numbers above hers. Thus this chart compares information from the death records of these two men named Kéri Mihály who lived in the same town and died about the same time with the information given on Juhász Erzsébet’s death record.

Comparing Death Information from Erzsébet and Two Men Named Mihály

I’ve highlighted in green that one of the men more closely fit the number of years of marriage while the other man more closely fit the number of years she would have been widowed.

I wasn’t any closer to determining which of these two men was her husband than I was before! But then….Look at the house numbers! When I added the house numbers to the chart, it became very clear that her husband was the Michael Keri who died on 30 September 1868.

Many records do not even list house numbers, and when they are listed, they are often ignored. That one little puzzle piece made all the difference in determining who this man was. In future weeks I’ll write how I put other puzzle pieces together until I formed a much clearer picture of this man named Michael Keri.


543 is made from three consecutive numbers so it is divisible by 3.

543 is the hypotenuse of the Pythagorean triple 57-540-543. Can you find the greatest common factor of those three numbers?

  • 543 is a composite number.
  • Prime factorization: 543 = 3 x 181
  • 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 543 has exactly 4 factors.
  • Factors of 543: 1, 3, 181, 543
  • Factor pairs: 543 = 1 x 543 or 3 x 181
  • 543 has no square factors that allow its square root to be simplified. √543 ≈ 23.30236

536 Family Reunion

Last week I attended a family reunion. My uncle Bob showed me a very clever way that helps him remember the number of children that my dad and each of his siblings had.

How Many Children

In case you are wondering, I was one of Leonard’s fifteen kids: He and his first wife had 4 children. They divorced. He met my mom who already had a child of her own. They married and had 6 children. She died. Then after he married my step-mother who already had two grown children, they had two more.

  • 536 is a composite number.
  • Prime factorization: 536 = 2 x 2 x 2 x 67, which can be written 536 = (2^3) x 67
  • The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 536 has exactly 8 factors.
  • Factors of 536: 1, 2, 4, 8, 67, 134, 268, 536
  • Factor pairs: 536 = 1 x 536, 2 x 268, 4 x 134, or 8 x 67
  • Taking the factor pair with the largest square number factor, we get √536 = (√4)(√134) = 2√134 ≈ 23.15167

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