This is just something that occured to me today; I haven’t yet had the time to really explore it. Once I do, I’m fairly certain that it’s range of use will expand however, for the time being, please note the limitation listed below.

Technique for performing mental multiplication for larger numbers.

This applies to any natural number that falls within 10 less than the next multiple of 50. For example, it will work with 248 but not 234; 495 but not 476, etc. There are definite patterns that emerge once you apply the technique to numbers outisde of this restriction, so I’m quite sure that I will be able to modify it to work with all natural numbers once I have a moment to look at it again… but for now, it’s a good quick trick for those ranges to which it applies.

Take your two numbers, I’ll use 497 and 343 as an example. For the purpose of clarity, let us refer to the first value; 497, as a and the second; 343, as b.

Round a and b to the nearest multiple of 50 and find their product:
500 x 350 = 175000

Next, take the difference of the rounded a minus a and multiply it by the rounded b:
500 - 497 = 3
3 x 350 = 1050
Let’s call that product x.

Now, do the same, but reverse a and b; rounded b minus b multiplied by a:
350 - 343 = 7
7 x 500 = 3500
Let’s call that product y.

Now, add x and y together and subtract the sum from your initial product of the rounded values:
1050 + 3500 = 4550
175000 - 4550 = 170450

We’re almost there. The last step is to find the product of the difference of the ones from 10 in the first values…so:
497, the value of ones is 7, so:
10 - 7 = 3
343, the value of ones is 3, so:
10 - 3 = 7
Now, find the product of those differences:
3 x 7 = 21

Add this to the large product above and you have your answer:
170450 + 21 = 170471

I’ll leave it to you to explore this technique on larger numbers with more digits.

It may look tiedious when written out in this manner, but it’s quite quick and easy to follow when running through the steps in your head.

Hope that helps!

Let’s use 18 and 19 as an example.

Add the second digit in one of the numbers to the other number.
18 + 9 = 27
Now, add a zero (mulitply by 10)
27 x 10 = 270
Multiply the last digit of each number
8 x 9 = 72
Add the two values together
270 + 72 = 342

18 x 19 = 342

So, just in case any one else out there is having the same issue, I thought I’d share the function that I ended up writing. It does the job quite nicely.


Function convertTime(i As String)
' D'Arcy Gregoire
' October 24, 2007
'
Dim hVal As Double
Dim hInt As Double
Dim hDec As Double
Dim hFin As String
Dim mVal As Double
Dim mInt As Integer
Dim mDec As Double
Dim mFin As String
Dim sVal As Double
Dim sInt As Integer
Dim sFin As String

End Function


mod_rewrite code:
RewriteEngine on
RewriteCond %{HTTP_REFERER} !^$
RewriteCond %{HTTP_REFERER} !^http://(www\.)?yourdomain.com(/)?.*$ [NC]
RewriteRule .*\.(gif|jpg|jpeg|bmp)$ http://yourdomain.com/default_image.jpe [R,NC]

If that doesn’t work quite like you would have expected, try removing the line that says RewriteEngine on and adding Options +FollowSymlinks in it’s place. If that doesn’t work, take them both out and try that. If it still won’t work, try just putting both of those lines back in together. One of those combinations will work.

Just paste one of these into your .htaccess file. Most FTP applications can’t see the .htaccess file, so don’t worry… just name it htaccess.txt on your computer, upload it, and then rename it to .htaccess and it will work. Of course, you’ll need to put your domain name where it says yourdomain.com and the default image that you want to have displayed where it says http://yourdomain.com/default_image.jpe
Notice that I’ve made the default image a .jpe file, since we haven’t restricted this file type. If you we’re to make the default image one of the restricted file types (.gif, .jpg, .jpeg, or .bmp in the example above), it would just throw it into a loop since it wouldn’t be allowed to show the default image, so it would try to show the default image, but it wouldn’t be allowed… and so on…
Good luck, hope this helps someone out.