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If you are like me, you have an appreciation of mathematics, and
enjoy seeing how a mathematical formula can be applied to real-world
situations. And, of course, love math tricks and fun math games!
Even those who are not so enthusiastic about math, they are invited
too! In fact, I challenge anybody who does not like math to look over
these number tricks posts and not go away with a new-found appreciation
of mathematics!
For those parents out there with kids who find arithmetic boring, you are encouraged to look over the material in math tricks; you will be sure to find something that your kids will enjoy – and get them interested in math!
but I would not go that far. It is, however, a very interesting number.
Indeed, the number 6174 is also known as the Kaprekar constant, named
after the Indian mathematician Dattaraya Ramchandra Kaprekar who studied
the mystery behind 6174.
So what is all the hoopla about 6174? Well, first, if you arrange the
digits such that you have the highest number (7641) and also the lowest
number (1467), and then determine the difference between the two, you
arrive at 6174 (7641 – 1467 = 6174).
Well you say, I suppose this is somewhat interesting. But now suppose
you take the number 2355. Do what you did before with 6174 – rearrange
the numbers to obtain the highest and lowest numbers, and then subtract
the lowest from the highest:
2355 -> 5532, 2355
5532 – 2355 = 3177
Now continue the process with the result:
3177 -> 7731, 1377
7731 – 1377 = 6354
And again:
6354 -> 6543, 3456
6543 – 3456 = 3087
Continuing:
3087 -> 8730, 0378
8730 – 378 = 8352
8352 -> 8532, 2358
8532 – 2358 = 6174
As you can see, this process leads to a convergence to 6174. And as
you saw before, performing this routine on 6174 results in an endless
loop. Cool!
In fact, this same result will occur for any four digit number you
choose as long as the number isn’t composed of the same digit (eg., 4444
would not work). You can even use leading zero’s for your four digit
number (eg., 0007). Now that is interesting!
Let’s try another example, one with a lot of zeros – 3000:
3000 -> 3000, 0003
3000 – 3 = 2997
2997 -> 9972, 2799
9972 – 2799 = 7173
7173 -> 7731, 1377
7731 – 1377 = 6354
6354 -> 6543, 3456
6543 – 3456 = 3087
087 -> 8730, 0378
8730 – 378 = 8352
8352 -> 8532, 2358
8532 – 2358 = 6174
It is this process that was discovered by our Indian friend Kaprekar,
and is known as Kaprekar’s routine. There are other similar numbers
that are obtained for other n-digit numbers. For example, for three
digit numbers, this process leads to a convergence to 495. Using the
routine on two digit numbers results in an infinite loop:
9 -> 81 -> 63 -> 27 -> 45 -> 9
As an interesting experiment, you are invited to try to determine
what happens if you perform this routine on higher digit numbers. You
may be surprised to see what your results are!
enjoy seeing how a mathematical formula can be applied to real-world
situations. And, of course, love math tricks and fun math games!
Who is Math Tricks for?
This site is for anybody, really. Young or old, rich or poor, it does not matter.too! In fact, I challenge anybody who does not like math to look over
these number tricks posts and not go away with a new-found appreciation
of mathematics!
For those parents out there with kids who find arithmetic boring, you are encouraged to look over the material in math tricks; you will be sure to find something that your kids will enjoy – and get them interested in math!
The Mystery of 6174
6174. It is a number well known to many. Some say it is mysterious,but I would not go that far. It is, however, a very interesting number.
Indeed, the number 6174 is also known as the Kaprekar constant, named
after the Indian mathematician Dattaraya Ramchandra Kaprekar who studied
the mystery behind 6174.
So what is all the hoopla about 6174? Well, first, if you arrange the
digits such that you have the highest number (7641) and also the lowest
number (1467), and then determine the difference between the two, you
arrive at 6174 (7641 – 1467 = 6174).
Well you say, I suppose this is somewhat interesting. But now suppose
you take the number 2355. Do what you did before with 6174 – rearrange
the numbers to obtain the highest and lowest numbers, and then subtract
the lowest from the highest:
2355 -> 5532, 2355
5532 – 2355 = 3177
Now continue the process with the result:
3177 -> 7731, 1377
7731 – 1377 = 6354
And again:
6354 -> 6543, 3456
6543 – 3456 = 3087
Continuing:
3087 -> 8730, 0378
8730 – 378 = 8352
8352 -> 8532, 2358
8532 – 2358 = 6174
As you can see, this process leads to a convergence to 6174. And as
you saw before, performing this routine on 6174 results in an endless
loop. Cool!
In fact, this same result will occur for any four digit number you
choose as long as the number isn’t composed of the same digit (eg., 4444
would not work). You can even use leading zero’s for your four digit
number (eg., 0007). Now that is interesting!
Let’s try another example, one with a lot of zeros – 3000:
3000 -> 3000, 0003
3000 – 3 = 2997
2997 -> 9972, 2799
9972 – 2799 = 7173
7173 -> 7731, 1377
7731 – 1377 = 6354
6354 -> 6543, 3456
6543 – 3456 = 3087
087 -> 8730, 0378
8730 – 378 = 8352
8352 -> 8532, 2358
8532 – 2358 = 6174
It is this process that was discovered by our Indian friend Kaprekar,
and is known as Kaprekar’s routine. There are other similar numbers
that are obtained for other n-digit numbers. For example, for three
digit numbers, this process leads to a convergence to 495. Using the
routine on two digit numbers results in an infinite loop:
9 -> 81 -> 63 -> 27 -> 45 -> 9
As an interesting experiment, you are invited to try to determine
what happens if you perform this routine on higher digit numbers. You
may be surprised to see what your results are!
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