Originally Posted by
manker
OK. It can be proved by simplification.
The first step is multiplying by 8 (2X2X2); cancel out step 7 by removing one of the twos.
Step 5 is also cancelled because you've gotten rid of the divisor of two at the end so you must not add the last three digits a second time.
This means that step seven is gone, step 5 is gone and you're multiplying by 4 in the first instance.
We now have
1 Multiply first 3 digits by 4
2 Add 1
3 Multiply by 250
4 Add last three digits
5 Subtract 250
Still works, right?
Steps 2 and 5 cancel themselves out since adding one before multiplying by 250 has the effect of adding 250 to the figure.
We now have
1 Multiply first 3 numbers by 4
2 Multiply by 250
3 Add last 3 digits
Since 4*250= 1000 we may as well simplify further and get rid of step 2 by making step one the first 3 numbers*1000
Now we're left with
1 Multiply the first 3 numbers by 1000
2 Add last 3 digits.
The above is moving the 3 digit number 3 decimal places to the left and slotting in the last 3 digits.
=> It works for everyone.
Note: It's the same principle for 7 digit numbers, it just cancels down to multiplying by 10000 rather than 1000 in it's simplest form.
Bookmarks