Lets talk about amazing.
11-20-2003, 08:15 AM
#13
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Originally posted by Baja Daze
Not Amazing, just simple arithmetic!
Okay, let's take your first 3 digits...Let's say it's ABC. This number can be expressed as A-Hundreds plus B-tens plus C. Follow me so far.
Okay, so this equals:
100A + 10B + C
When we multiple by 80 (Hmmm...I wonder where 80 came from, we'll see soon) we have:
8000A + 800B + 80C
Okay, Now we must add 1, so we have:
8000A + 800B + 80C + 1
Now we multiply by 250, so this leaves:
2000000A + 200000B + 20000C + 250
(You can now begin to see why 80 was chosen...nice round numbers that are 2 times multiples ot 10. Also, note the 250 term at the end.)
Okay, next we must add our last four digits. Let's say my last four digits are DEFG. This number is in the thousands and can be expressed as:
1000D + 100E + 10F +G
So, when we add it to what we were left with before, we have:
(2000000A + 200000B + 20000C + 250) + (1000D + 100E + 10F +G)
We add it again and now have:
(2000000A + 200000B + 20000C + 250) + (1000D + 100E + 10F +G) + (1000D + 100E + 10F +G)
This can be reduced to:
(2000000A + 200000B + 20000C + 250) + 2(1000D + 100E + 10F +G)
When we multiply through by our by two:
(2000000A + 200000B + 20000C + 250) + (2000D + 200E + 20F +2G)
(How convenient, all the terms are now two times multiples of ten)
Anyway, now we subtract our 250(remember that) and the positive 250 term goes away:
(2000000A + 200000B + 20000C) + (2000D + 200E + 20F +2G)
All that's left is to divide by 2(imagine that), so we are left with:
(1000000A + 100000B + 10000C) + (1000D + 100E + 10F +G)
Voilla: Add the terms up and we have a number that looks like:
ABCDEFG
Not Amazing, just simple arithmetic!
Okay, let's take your first 3 digits...Let's say it's ABC. This number can be expressed as A-Hundreds plus B-tens plus C. Follow me so far.
Okay, so this equals:
100A + 10B + C
When we multiple by 80 (Hmmm...I wonder where 80 came from, we'll see soon) we have:
8000A + 800B + 80C
Okay, Now we must add 1, so we have:
8000A + 800B + 80C + 1
Now we multiply by 250, so this leaves:
2000000A + 200000B + 20000C + 250
(You can now begin to see why 80 was chosen...nice round numbers that are 2 times multiples ot 10. Also, note the 250 term at the end.)
Okay, next we must add our last four digits. Let's say my last four digits are DEFG. This number is in the thousands and can be expressed as:
1000D + 100E + 10F +G
So, when we add it to what we were left with before, we have:
(2000000A + 200000B + 20000C + 250) + (1000D + 100E + 10F +G)
We add it again and now have:
(2000000A + 200000B + 20000C + 250) + (1000D + 100E + 10F +G) + (1000D + 100E + 10F +G)
This can be reduced to:
(2000000A + 200000B + 20000C + 250) + 2(1000D + 100E + 10F +G)
When we multiply through by our by two:
(2000000A + 200000B + 20000C + 250) + (2000D + 200E + 20F +2G)
(How convenient, all the terms are now two times multiples of ten)
Anyway, now we subtract our 250(remember that) and the positive 250 term goes away:
(2000000A + 200000B + 20000C) + (2000D + 200E + 20F +2G)
All that's left is to divide by 2(imagine that), so we are left with:
(1000000A + 100000B + 10000C) + (1000D + 100E + 10F +G)
Voilla: Add the terms up and we have a number that looks like:
ABCDEFG
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11-20-2003, 12:02 PM
#17
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Location: Austin, Texas
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Just to make things a little easier...
#7 cancels out #3 and #4:
1 times 250 minus 250 equals 0.
#2, #4, and #8 get the first three digits into the 10,000 position:
80 times 250 divided by 2 equals 10,000
#8 cancels out #6:
(last four plus last four) divides by 2 equals last four
So..... you have the first three digits "shifted" four places (times 10,000) and the last four digits are unchanged.
Simple really...
#7 cancels out #3 and #4:
1 times 250 minus 250 equals 0.
#2, #4, and #8 get the first three digits into the 10,000 position:
80 times 250 divided by 2 equals 10,000
#8 cancels out #6:
(last four plus last four) divides by 2 equals last four
So..... you have the first three digits "shifted" four places (times 10,000) and the last four digits are unchanged.
Simple really...
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