DNA and Big Brother

/ ivasallay / 2 Comments

When my husband was a little baby, his dad filled out the genealogy section in his baby book in his beautiful, distinct handwriting:

Even though most of the pages are blank, my husband has always cherished that book, and it has been extremely helpful in finding many other of his ancestors.

From additional research, we have learned that my husband’s grandfather, Frank Kovach, was born Kovács Ferenc in Szürte, Ung County, Hungary. That little town has had several border changes and is now part of Ukraine, but still only about eight miles from the Hungarian border. You can see a map showing the location of Szürte in a post I wrote a couple of years ago. Ferenc (Frank) was born 13 June 1883 to Kovács Péter and Péntek Mária – that’s their names in Hungarian name order. The baby book gives their names in English name order. My husband remembers his grandfather, Frank, vividly. He died 10 June 1968 in Ontario, San Bernardino, California.

Many years ago when I tried to figure out Frank’s place of birth, I found three other people whose parents had the same names as his parents. Could they be Frank’s siblings? Could the two boys be his big brothers? (You will need to be logged into FamilySearch.org and Ancestry.com to see most of the links I’ve included in this post.)

  1. Julia Kovach (Kovács Juliánna) was born 12 Apr 1882 in Hungary (both of her parents were born in Ung County, Hungary!). She died 15 Jun 1940 in Cleveland, Ohio. Maybe Frank was also born in Ung County, I excitedly thought! Several years later I found a death record for one of Frank’s sons that gave the specific town in Ung county where Frank was born. Still years after that I found Frank’s petition for naturalization also confirming it.
  2. Steven Kovach (Kovács István) was born about 1874 in Hungary. He married Julia Csengeri on 22 Sept 1901 in New York.

    He MAY have died seventeen years later on 11 Dec 1918 in Union, Washington, Pennsylvania, but buried in Cleveland, Ohio.  The father on that death certificate was Pete Kovacs and the mother was Mary Pantik. The certificate says he is married, but there was no place to write his wife’s name on it. The informant was Steve Kovach, which just happens to be Frank’s sister’s (Julia Kovach) husband’s name, so his brother-in-law might have actually been the informant. Julia and Steve lived in Cleveland, and the deceased, Steve, was buried in Cleveland even though he died in Pennsylvania.
  3. John Kovacs (Kovács János) was born 23 Jan 1870 in Hungary. He died 29 Oct 1943 in Cleveland. To fully appreciate the information for John, we need to look at his and his wife’s death certificates side by side.

Notice that the address for both John and Veronica is 9012 Cumberland, so that helps to establish that they were husband and wife even though the spellings of their last names are not exactly the same. This is important since there were MANY men named John Kovach in Cleveland. The couple’s shared tombstone confirms the dates given above. On Veronica’s death certificate, her father is listed as John Daniels and the informant is Dale Kovats. Further research establishes that Dale is John and Veronica’s son, and the 1940 census shows Dale and his wife, Rose at the bottom of the page, and their daughter and some of Rose’s relatives on the top of the next page. Dale is the key to this puzzle because Dale has a descendant who is a 3rd to 4th cousin DNA match to my husband! That means that John Kovacs is indeed Frank’s big brother, and I am in tears as I am finally able to positively make that statement.

Ancestry.com explains “Our analysis of your DNA predicts that this person you match with is probably your third cousin. The exact relationship however could vary. It could be a second cousin once removed, or perhaps a fourth cousin. While there may be some statistical variation in our prediction, it’s likely to be a third cousin type of relationship—which are separated by eight degrees or eight people. However, the relationship could range from six to ten degrees of separation.” (bold print added)

My husband, Steven, and this DNA match are separated by seven degrees.

Was big brother John also born in Szürte? It seems likely, but he may have also been born about 3 miles away in Kholmetz where a 4th-6th cousin DNA shared match traces her ancestry. If only I could get into the Szürte Reformed Church records and Kholmetz records to look for a Kovács János (John Kovacs) born on 23 Jan 1870 as well as the records for the others and certainly a few more siblings as well!

 

1392 and Pythagorean Triples

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1392 is the hypotenuse of ONE Pythagorean triple, 960-1008-1392.

However, 1392 is the leg of so many Pythagorean triples, that it is possible I haven’t listed them all in this graphic:


Why is it the hypotenuse only once, but it is a leg so many times?

Because of its factors!

  • 1392 is a composite number.
  • Prime factorization: 1392 = 2 × 2 × 2 × 2 × 3 × 29, which can be written 1392 = 2⁴ × 3 × 29
  • 1392 has at least one exponent greater than 1 in its prime factorization so √1392 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1392 = (√16)(√87) = 4√87
  • The exponents in the prime factorization are 4, 1 and 1. Adding one to each exponent and multiplying we get (4 + 1)(1 + 1)(1 + 1) = 5 × 2 × 2 = 20. Therefore 1392 has exactly 20 factors.
  • The factors of 1392 are outlined with their factor pair partners in the graphic below.

1392 has only one prime factor that leaves a remainder of one when it is divided by four. That factor is 29. It makes 960-1008-1392 simply (20-21-29) times 48. Easy Peasy.

ONE of the reasons it is a leg so many times is because several of its factors are in primitive Pythagorean triples, and multiplying those triples by that factor’s factor pair gives us a triple with 1392 as a leg:

  • (3-4-5) times 464 is (1392-1856-2320)
  • (3-4-5) times 348 is (1044-1392-1740)
  • (8-15-17) times 174 is (1392-2610-2958)
  • (5-12-13) times 116
  • (12-35-37) times 116, and so on

Another reason is every Pythagorean triple can be written in this form 2ab, a²-b², a²+b², and 1392 = 2(696)(1) or 2(348)(2) or 2(232)(3) or 2(174)(4) and so on.

The last reason is that since 1392 has six factor pairs in which both factors are even, it can be written as a²-b²: (The average of the two numbers in the factor pair gives us the first number to be squared. Subtract the second number from it to get the second number to be squared.)

  • 696 and 2 give us 349² – 347² = 1392
  • 348 and 4 give us 176² – 172² = 1392
  • 232 and 6 give us 119² – 113² = 1392
  • 174 and 8 give us 91² – 83² = 1392
  • 116 and 12 give us 64² – 52² = 1392
  • 58 and 24 give us 41² – 17² = 1392

Some of the triples can be found by more than one of the processes listed above. It can be very confusing to keep track of them all. That is why I usually only write when a number is the hypotenuse of a triple and not when it is a leg.

 

 

1391 and Level 1

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Many of the clues in this puzzle have double digits. If you know why they do, then you can find all the factors and solve this puzzle!

Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Here’s some information about the number 1391:

  • 1391 is a composite number.
  • Prime factorization: 1391 = 13 × 107
  • 1391 has no exponents greater than 1 in its prime factorization, so √1391 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1391 has exactly 4 factors.
  • The factors of 1391 are outlined with their factor pair partners in the graphic below.

1391 is the hypotenuse of a Pythagorean triple:
535-1284-1391 which is (5-12-13) times 107

1390 Find the Factors (ax±b)(cx±d)

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I liked making a puzzle using trinomials earlier today. This one will take more skill to solve even though it contains fewer trinomials. Some of the factors will have negative numbers, and the leading coefficients of the trinomials are not 1.

In this puzzle, you can see the number 24 twice. It needs to be factored to solve the puzzle. It might be 3 × 8 or 4 × 6, but it can’t be 1 × 24 or 2 × 12 because for this puzzle ALL of the factors of 24 have to be non-zero integers from -10 to +10.

Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Every factor must appear once in the first column and once in the top row. So if you put 2x + 5 in the top row, you will also have to put 2x + 5 somewhere in the first column as well.

Sometimes all of the terms in the trinomial have a common factor and can, therefore, be factored further, but don’t worry about that right now.

You will have to find all of the factors in the puzzle before you can figure out what the missing clue should be. That’s about all the mystery I can put in a puzzle like this. Good luck with it!

Since this is different than any other puzzle I’ve ever published, you can see the solution here:

Now I’ll share some information about the number 1390:

  • 1390 is a composite number.
  • Prime factorization: 1390 = 2 × 5 × 139
  • 1390 has no exponents greater than 1 in its prime factorization, so √1390 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 1390 has exactly 8 factors.
  • The factors of 1390 are outlined with their factor pair partners in the graphic below.

1390 is the hypotenuse of a Pythagorean triple:
834-1112-1390 which is (3-4-5) times 278

1390 is 102345 in BASE 6 making it the smallest number to use all the digits less than 6 in base 6. Thank you OEIS.org for that reminder.

1389 Positive Trinomial Puzzle

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Today on Twitter, Mr. Allen requested some good problem-solving resources for quadratics. He made up one himself.

I decided to make one as well. It is similar to my other Find the Factors puzzles. You will have to use logic to solve it, but in many ways, it will be easier to solve than most of my regular puzzles. Like always, there is only one solution.

Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Every term is positive so if you already know how to factor trinomials it should be relatively easy to solve. All the factors from (x + 1) to (x + 9) need to appear exactly one time in both the first column and the top row of the puzzle.  Once all the factors are found, the puzzle is solved, but you can find all the products of those factors and write them in the body of the puzzle if you want.

Since this is my 1389th post, here’s a little bit about that number:

  • 1389 is a composite number.
  • Prime factorization: 1389 = 3 × 463
  • 1389 has no exponents greater than 1 in its prime factorization, so √1389 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1389 has exactly 4 factors.
  • The factors of 1389 are outlined with their factor pair partners in the graphic below.

1389 is the difference of two squares in two different ways:
695² – 694² = 1389
233² – 230² = 1389

1388 Mystery Level

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Sometimes puzzles start out easy enough but get a little more complicated later on. Does that happen with this puzzle? There’s only one way to find out!


Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Here are some facts about the number 1388:

  • 1388 is a composite number.
  • Prime factorization: 1388 = 2 × 2 × 347, which can be written 1388 = 2² × 347
  • 1388 has at least one exponent greater than 1 in its prime factorization so √1388 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1388 = (√4)(√347) = 2√347
  • 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 1388 has exactly 6 factors.
  • The factors of 1388 are outlined with their factor pair partners in the graphic below.

1388 is the difference of two squares:
348² – 346² = 1388

The Shape of 1387 Tiny Squares

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22³ – 21³ = 1387, and that’s why it is the 22nd hexagonal number.

1387 is also the 19th decagonal number. Why? Because 4(19²) – 3(19) = 1387.

Here’s more about the number 1387:

  • 1387 is a composite number.
  • Prime factorization: 1387 = 19 × 73
  • 1387 has no exponents greater than 1 in its prime factorization, so √1387 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1387 has exactly 4 factors.
  • The factors of 1387 are outlined with their factor pair partners in the graphic below.

 

1387 is the hypotenuse of a Pythagorean triple:
912-1045-1387 which is 19 times (48-55-73)

1386 What You Need to Know About the Multiplication Game

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Helpful Hints about the Multiplication Game:

I recently wrote about Hooda Math’s Multiplication Game. There’s a couple of things I didn’t tell you in that post.

First of all, you don’t have to use a computer to play the game. (However, using one the first time you play will help you understand how to play). You can print a game board to play. I’ve created a game board below that you could use. Each player can use different items such as beads, pennies, nickels, and dimes as markers to mark the factors used and to claim the resulting products on the game board.

The second thing you should know is that getting four squares in a row, horizontally, vertically or diagonally is NOT equally likely every place on the board. If one particular number is all you need to get a win, you are less likely to get that number if it only has one factor (like the numbers marked in yellow have). As far as this game is concerned, the products have the number of factors that I’ve indicated, even though in reality most of them have more than that.

You can’t win unless your opponent gives you one of the factors you need to claim that winning space. If 4 of the 9 possible factors will get it for you, the odds are much better your opponent will give you what you need than if only 1 of the 9 possible factors will do it.

If you know which numbers have four possible factors, you may have an advantage over someone who thinks this game is really just a variation of tic-tac-toe. Of course, those products with four factors could also make you more likely to get blocked as well! And if you use my colorful game board, your opponent will know just as much as you do about how many ways they can get each square.

1386 Factor Cake:

Since the biggest prime factor of 1386 is 11, it makes an especially festive factor cake!

Factors of 1386:

Now I’ll share some information about the number 1386:

  • 1386 is a composite number.
  • Prime factorization: 1386 = 2 × 3 × 3 × 7 × 11, which can be written 1386 = 2 × 3² × 7 × 11
  • 1386 has at least one exponent greater than 1 in its prime factorization so √1386 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1386 = (√9)(√154) = 3√154
  • The exponents in the prime factorization are 1, 2, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(2 + 1)(1 + 1)(1 + 1) = 2 × 3 × 2 × 2 = 24. Therefore 1386 has exactly 24 factors.
  • The factors of 1386 are outlined with their factor pair partners in the graphic below.

Sum-Difference Puzzle:

1386 has twelve factor pairs. One of the factor pairs adds up to 85, and a different one subtracts to 85. If you can identify those factor pairs, then you can solve this puzzle!

One More Fact about the Number 1386:

OEIS.org also noted that 1 + 3⁴ + 8 + 6⁴ = 1386.

1385 Mystery Level

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You can suspect that the common factor of 9 and 6 is either 1 or 3, but don’t jump to conclusions about which one will satisfy this mystery! There’s important evidence elsewhere in the puzzle that you should consider first.

Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Now I’ll share some facts about the puzzle number, 1385:

  • 1385 is a composite number.
  • Prime factorization: 1385 = 5 × 277
  • 1385 has no exponents greater than 1 in its prime factorization, so √1385 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1385 has exactly 4 factors.
  • The factors of 1385 are outlined with their factor pair partners in the graphic below.

1385 is the sum of two squares in two different ways:
32² + 19² = 1385
37² + 4² = 1385

1385 is the hypotenuse of a Pythagorean triple:
296-1353-1385 calculated from 2(37)(4), 37² – 4², 37² + 4²
575-1260-1385 which is 5 times (115-252-277)
663-1216-1385 calculated from 32² – 19², 2(32)(19), 32² + 19²
831-1108-1385 which is (3-4-5) times 277

1384 and Level 6

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Guessing and checking can be so frustrating! If instead, you study the clues to find a logical place to start this puzzle, you are more likely to be able to find the one and only solution.

Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Here are a few facts about the number 1384:

  • 1384 is a composite number.
  • Prime factorization: 1384 = 2 × 2 × 2 × 173, which can be written 1384 = 2³ × 173
  • 1384 has at least one exponent greater than 1 in its prime factorization so √1384 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1384 = (√4)(√346) = 2√346
  • The exponents in the prime factorization are 3 and 1. Adding one to each exponent and multiplying we get (3 + 1)(1 + 1) = 4 × 2 = 8. Therefore 1384 has exactly 8 factors.
  • The factors of 1384 are outlined with their factor pairs in the graphic below.

1384 is the hypotenuse of a Pythagorean triple:
416-1320-1384 which is 8 times (52-165-173)