A Multiplication Based Logic Puzzle

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.


Comments on: "861 Interpolating Genealogical Data" (4)

  1. Fascinating stories! Very large families are common in my ancestry too, and as in your examples many of the children seem to have died in infancy. They can be just a collection of names and dates. Or, as you have done, it is possible to breathe life into those names and imagine how those people must have lived and felt.

    Liked by 1 person

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