Comments for Math Tricks http://mathtricks.org Math Tricks + Math Games = Math Fun! Thu, 12 Apr 2012 21:54:15 +0000 hourly 1 http://wordpress.org/?v=3.3.2 Comment on The Fantastic 6174 by Lesego http://mathtricks.org/mysterious-numbers/the-fantastic-6174/comment-page-1/#comment-370 Lesego Thu, 12 Apr 2012 21:54:15 +0000 http://mathtricks.org/?p=788#comment-370 I'm not a mathematician or anything but I do find this very interesting. I would like help with solving the equation (if there is any) to get the other n-digit numbers. 2-digits : 9 or the loop shown 3-digits : 495 4-digits : 6174 5-digits : 61974 6-digits : 851742 I'm trying to find the equation that can give me the numbers for any number of digits (nth-digit). I'm not sure of it exists but I'm trying to incorporate 9 in the equation. Please help. Thanks :) I’m not a mathematician or anything but I do find this very interesting.

I would like help with solving the equation (if there is any) to get the other n-digit numbers.

2-digits : 9 or the loop shown
3-digits : 495
4-digits : 6174
5-digits : 61974
6-digits : 851742

I’m trying to find the equation that can give me the numbers for any number of digits (nth-digit).

I’m not sure of it exists but I’m trying to incorporate 9 in the equation. Please help.

Thanks :)

]]> Comment on Math Brain Teaser – Extra Space by Shayz http://mathtricks.org/math-tricks/math-brain-teaser-extra-space/comment-page-1/#comment-369 Shayz Wed, 11 Apr 2012 03:40:16 +0000 http://mathtricks.org/?p=203#comment-369 The slopes of the hypotenuse for both the red and green triangles are slightly different, causing the hypotenuse of the first triangle to bend in, and the hypotenuse of the second triangle to bend out. The slope of the green triangle is 2/5 and the slope of the red triangle is 3/8 To test this, put a straightedge up to the picture from the top right corner to the bottom left, and you will see how the hypotenuse is ever so slightly bent at the junction of these two different slopes The slopes of the hypotenuse for both the red and green triangles are slightly different, causing the hypotenuse of the first triangle to bend in, and the hypotenuse of the second triangle to bend out.

The slope of the green triangle is 2/5 and the slope of the red triangle is 3/8

To test this, put a straightedge up to the picture from the top right corner to the bottom left, and you will see how the hypotenuse is ever so slightly bent at the junction of these two different slopes

]]> Comment on The Fantastic 6174 by Garrett Hildebrand http://mathtricks.org/mysterious-numbers/the-fantastic-6174/comment-page-1/#comment-366 Garrett Hildebrand Wed, 04 Apr 2012 21:57:28 +0000 http://mathtricks.org/?p=788#comment-366 I now agree with the statement that with the exception of numbers composed of the same digit (only 10 of them), all others will yield 6174. That makes this number even more remarkable to me! The zero results I was seeing turn out to be a bug in my code. What was happening is that although I made sure the initial number was R#4 (right-justified in a field of zeroes), I was not doing this on the subtraction result. Consequently, certain number combinations would yield 999 as a result (for example, 5554 and 5556). So instead of subtracting 999 from 9990, it was subtracting 999 from 999. I now agree with the statement that with the exception of numbers composed of the same digit (only 10 of them), all others will yield 6174. That makes this number even more remarkable to me!

The zero results I was seeing turn out to be a bug in my code.

What was happening is that although I made sure the initial number was R#4 (right-justified in a field of zeroes), I was not doing this on the subtraction result. Consequently, certain number combinations would yield 999 as a result (for example, 5554 and 5556). So instead of subtracting 999 from 9990, it was subtracting 999 from 999.

]]> Comment on The Fantastic 6174 by Garrett Hildebrand http://mathtricks.org/mysterious-numbers/the-fantastic-6174/comment-page-1/#comment-365 Garrett Hildebrand Tue, 03 Apr 2012 22:12:18 +0000 http://mathtricks.org/?p=788#comment-365 I created a program to go through all 10,000 possible numbers. What I found out is that there are 383 numbers that when factored-out (high digits to low, low digits to high) yield 20 unique pairs that produce the Kaprekar constant in one subtraction. I also found out that there are certain numbers that take 7 iterations of the algorithm to produce the expected result. This was an unexpected side-benefit of my wondering, "how many of the 10,000 possible numbers produce a zero result?" I have found that exactly 80 numbers will produce a zero result with this process (including ones such as 1111, 2222, 3333, etc., that we already knew about). Here are 8 in the 2xxx range: 2111 2122 2212 2221 2222 2223 2232 2322 2333 There are only 4 in the 9xxx range: 9888 9899 9989 9998 If you are interested in all the details of this, send me an email. I wrote the whole thing up with all numbers included to share with some friends who are into math. But it is kind of long to post here. I would also be glad to share the program. It is written in Perl. I created a program to go through all 10,000 possible numbers. What I found out is that there are 383 numbers that when factored-out (high digits to low, low digits to high) yield 20 unique pairs that produce the Kaprekar constant in one subtraction. I also found out that there are certain numbers that take 7 iterations of the algorithm to produce the expected result. This was an unexpected side-benefit of my wondering, “how many of the 10,000 possible numbers produce a zero result?”

I have found that exactly 80 numbers will produce a zero result with this process (including ones such as 1111, 2222,
3333, etc., that we already knew about).

Here are 8 in the 2xxx range:

2111
2122
2212
2221
2222
2223
2232
2322
2333

There are only 4 in the 9xxx range:

9888
9899
9989
9998

If you are interested in all the details of this, send me an email. I wrote the whole thing up with all numbers included to share with some friends who are into math. But it is kind of long to post here. I would also be glad to share the program. It is written in Perl.

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