## A Multiplication Based Logic Puzzle

### 111 and How Well Can You Add and Subtract in All Those Foreign Languages in Which You’ve Learned How to Count?

111  is a composite number. 111 = 1 x 111 or 3 x 37. Factors of 111: 1, 3, 37, 111. Prime Factorization: 111 = 3 x 37.

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

111 = (1 + 2 + 3 + . . . + 35 +36)/6, which can be more easily calculated by using 111 = (36 x 37)/(2 x 6). Therefore, 111 is the magic sum of any 6 x 6 magic square that contains all the integers from 1 to 36.

One plus three equals what in Hungarian?

In general adults understand how to add and subtract one-digit numbers, and most adults also have learned how to count in at least one language other than their native language. Does that mean these adults can add and subtract in those other languages in which they have learned how to count? I am curious to know the answer to that question. Let me tell you how counting, adding, and subtracting in a foreign language work for me.

I studied Spanish for three years in High School. I remember doing some basic addition and subtraction problems back then. Even though I remember very little Spanish vocabulary, I can still add and subtract one-digit numbers in Spanish fairly well.

I studied German for one and a half years in college. I remember even less German than I remember Spanish. All of the number words LOOK familiar, but I failed miserably when I tried to add and subtract using German numbers.

I lived in Turkey for two years when my husband was stationed at Incirlik Air Base near Adana. I learned a bit of vocabulary and how to count in Turkish. I actually remember the Turkish numbers a little better than the German ones, but my ability to add and subtract in Turkish isn’t much better.

Now I am motivated to learn Hungarian. (I want to be able to understand my husband’s relatives better someday when I get to visit them in Hungary again.) The numbers in Hungarian are fresh in my mind, and I have even passed the time counting up to 1000 in Hungarian when I had nothing else to do.

When it came to doing basic addition or subtraction in Hungarian at this game site I found my ability to count did not help as much as I supposed. However with PRACTICE, I have been able to greatly improve my ability to add and subtract in Hungarian.

After gaining the ability to add and subtract in Hungarian, I added another wrench to the process: I required myself to say complete number sentences in Hungarian instead of allowing English words like plus, minus, or equals to be used.From Hungarian Verbs & Essentials of Grammar I learned that there are a few ways to say a number sentence when adding in Hungarian. The easiest two ways to say 4 + 3 = 7 are “Négy meg három (az) hét” or “Négy plusz három (az) hét.” Subtraction is a little more complicated because different numbers take two different case endings, ból or ből, in order to maintain vowel harmony. 10 – 4 = 6 is “Tízből négy az hat.” while 6 – 2 = 4 is “Hatból kettő az négy.”

Requiring myself to use complete Hungarian sentences has made me a little slower, and sometimes the hourglass empties before I click next to the correct number word. However, with PRACTICE I am getting better, and I will move on to the number games that use numbers up to 20 and 100 very soon.

This activity reinforces my belief that practice really does make a difference. I can see the merits of children practicing basic number facts in English or any other language they can speak. The FIND THE FACTORS puzzles are an excellent way for people of all ages to practice basic multiplication and division facts.

If you would like to see how well you can add and subtract using these learning games in other languages go to http://www.digitaldialects.com/.

Select one of the 70 available languages (listed in alphabetical order from left to right), select Numbers 1 -12, and begin the adding and subtracting game in the chosen language. I would love to know how well you do, so try it and leave a comment if your results don’t embarrass you too much!

#### Comments on: "111 and How Well Can You Add and Subtract in All Those Foreign Languages in Which You’ve Learned How to Count?" (8)

1. I’m interested by this arithmetic-in-other-languages sort of problem. While I did learn enough French to be able to count most of the way, back in middle school, somehow we never had to do anything mathematics with it and I hadn’t really noticed the lack before.

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• ivasallay said:

Maybe you’ve known French so long that it will just come naturally, maybe not. It will take some time for you to discover the answer for yourself. I can hardly wait to know what you find out!

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2. It never even occurred to me to do math in French. Just SAYING the numbers above ten was like a math problem (the word 80 in French can be translated as 4 20’s). It’s kind of a wild concept to do FrenchMath…I wonder how many areas of the brain that would tax. Deux many…But it’s a great idea.

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• ivasallay said:

That is really interesting how the French construct numbers over ten. I didn’t know that before. I wonder if it helps the French add and subtract any easier? Taxing the brain a little might be a good thing; overtaxing certainly wouldn’t be good. I hope you find it an enjoyable experience!

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• Taxing the brain, or overtaxing….so much depends on one’s own attitude towards it. Most of the days I welcome being challenged. But after 8 pm I am ready for brain candy.

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• It isn’t all the numbers over ten, but, for some reason French (in France) uses quatre-vingt (four-twenties) for 80 and quatre-vignt et dix (four-twenties and ten) for 90. French (in Belgium) has words for eighty and ninety that are more parallel to the words for multiples of ten up through seventy. I’ve heard that this, in French French, is a fossil from the time when numbers were counted in groups of twenty, but I don’t know whether that’s true.

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• There are still the very faintest echoes of this in English – “Three score years and ten”, for example.

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3. ivasallay said:

Four score and seven years ago…

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