My math teacher can add up 3 five-digit numbers in 2 seconds. How does he do it?

Question

Us students are stumped, and we can only add them in 20 seconds. Any ideas?

Answer 1

He probably practices mental math. That is how he does mental math very quickly. He has way more experience than you, being about 30 to 40 years older. Just practice adding and you can impress people with your skills!

Answer 2

Ironduke may have figured out the trick (although he doesn't explain it very completely. See an explanation at the bottom of this response.

If what your teacher is doing is not just a trick:

I would guess that your teacher is over 40 (maybe well over 40).
Today our schools have students use calculators so much that, although the students may have memorized their number facts, they don't get very good at them.
By contrast, when your teacher went to school, the students did a lot of drilling in arithmetic.
And your teacher has had a lot of years since to use those skills and get better at them.
And finally, your teacher happens to be exceptionally good at arithmetic.

A few comments:
1. The main trick is probably the ability to look at 3 numbers and immediately know the sum. You students should be able to do that with 2 numbers at a time, but it would take a lot of practice to memorize all the combinations of 3 numbers and be quick with the answers. Apparently your teacher has invested that time to become good at it.

2. While this particular skill is impressive, it probably isn't worth it to develop that type of speed with 3-at-a-time addition (except to impress and inspire each successive year's math students). Instead, you should become good at more routine calculations (2-at-a-time addition, multiplication of 2-digit numbers, etc.).

3. I am exceptionally good at mental arithmetic. I have won math competitions, and can routinely surprise people (including my college students) with my speed at mental math. But I could not do this particular type of problem in less than about 6 seconds, so your teacher is very, very good at it.

4. I'm almost 60, and there were no electronic calculators available until after I was out of college. Students today have no chance of developing as much speed as people my age, unless they throw their calculators away and practice, PRACTICE, P R A C T I CE!! And I don't suggest that you do that. You'd fall behind in understanding and performing the more complex calculations that require calculators.

5. Bottom line: You need to develop skill with a calculator, but:
a. You need to understand what the calculator is calculating; i.e., understand what addition, subtraction, multiplication and division mean, when to use each one, and what the answer means, so that you're not just a dummy pushing buttons and hoping for the right answer.
b. You should be able to do the simpler calculations in your head, so that you don't waste time pushing buttons when its faster to do it mentally. The more you can do in your head, the more THINKING you can do, as opposed to mindless BUTTON-PUSHING. Often you can enter fewer numbers into the calculator because you're doing some of the steps in your head.
c. You also need to be able to do somewhat more complex calculations in your head, for those times when your calculator isn't available (e.g., calculating your change when you make a purchase, calculating the total cost of items you are buying, or calculating the amount of sales tax on a purchase).
d. I have a trick (and it is a trick) where I multiply two 9-digit numbers in my head. If your teacher would like to learn that trick and impress next year's students, have him/her send me an e-mail.

And here's the trick that Ironduke is referring to:
The class chooses 2 of the numbers. The teacher chooses the other number (either the 2nd or the 3rd number, since it is based on one of the numbers chosen by the class).

The teacher's number is selected so that, when you add it to one of the student-chosen numbers, the total is 99,999.
Example: if the students choose 83947, the teacher writes 16052. (This doesn't work very well if the first digit of the students' number is 9, and it doesn't work at all if the students choose 99999. So you might try that if you want to mess up the trick.)

Then whatever the 3rd number is, the total is simply 100,000 plus that number minus 1. In other words, you write 1, followed by the first 4 digits of the number, and then its last digit minus 1.

Example:
35730
59375
40624
______
135729

Note that the total looks quite a bit like the first number, but with a 1 in front of it. In this case, the 3rd number is the one chosen by the teacher. The second and third numbers add up to 99,999, which is just 1 less than 100,000. So the total is just the first number, plus 100,000, minus 1. I made it a little more difficult by having the first number end in 0, so that when you subtract 1 it affects the last TWO digits.

Good luck to you in your math adventures!

Answer 3

Practice, Dewd.......... Practice ☺

Actually, there have always been people who could do those kinds of arithmetic acrobatics. The psychologists call them 'idiot-savants', which is a fancy way of saying 'one trick pony'. Most of the time, those people actually have only a rudimentary grasp of mathematics, and even they can't explain how they do it. And they're often kinda dull and leave one with the impression that they aren't the sharpest pencil in the box. (I'm trying desperately to remember the name of the movie about an autistic kid who cracked a super-secret government cypher system...... This gettin' old sucks ☺)

But, up until a hundred years or so ago, the word 'computer' used to have a *very* different meaning than it does today. It refered to one of those type people because every mathematics department in every University had one or two of them in the department to do the 'busy work' of long, drawn out computations. The ones that are still done by 'computer' today, only today its an electronic computer instead of biological one.

But the human mind is *still* the finest calculator in the known universe. You just have to figure out how to use it and then practice a lot. Math is like any other sport, you don't get good at it by setting on your αss watching somebody else play. You have to actually *do* it yourself.

HTH ☺

Doug

Answer 4

Does he say what the three numbers are before he adds them? Or does he write one down, let the class give the next number, and then he writes down the third number and then gives the sum almost instantaneously? If so, it is a trick that is as old as the hills.

Look at the answer and look at the first number to see if there is some correlation. There probably is one like the middle 3 digits of the answer are the same as the middle three digits of the first number.

Answer 5

Another possibility for speed if you guys are calling them out is that he adds the first two before the third one is ever heard.

This is only for real if he can do it off of a piece of paper with the three numbers neatly written down, starting from the time it is handed to him.

Answer 6

He is a math teacher and has been doing this forever.