1001 * 1001 = 1002001
1002 * 1001 = 1003002
1003 * 1001 = 1004003
...
1001 * 1002 = 1003002
1002 * 1002 = 1004004
1003 * 1002 = 1005006
...
1001 * 1003 = 1004003
1002 * 1003 = 1005006
1003 * 1003 = 1006009
...
Here is a pattern that makes it easy to calculate them quickly in the head:
1001 * 1001 = 1002001
1001 = 1000 + 1; keep 1 in your mind
1001 = 1000 + 1; again keep 1 in your mind
and now:
1001 * 1001 = (1001 + 1) & ...(1*1)
= 1002 & ...1
as ...1 must be a 3-digit number we concatenate 00 to it; so the result will be:
= 1002 & 00 & 1 = 1002001
This pattern can be applied for the other multiplications; for example:
1002 * 1003 = 1005006
1002 = 1000 + 2; keep 2 in your mind
1003 = 1000 + 3; keep 3 in your mind
and now:
1002 * 1003 = (1002+3) & 00 & (2*3)
= 1005006
As another example, let's try 1011 * 1008:
1011 = 1000 + 11; keep 11 in your mind
1008 = 1000 + 8; keep 8 in your mind
then:
1011 * 1008 = (1011+8) & ... & (11*8)
1011 * 1008 = 1019088
You can apply the same pattern for larger or smaller numbers (follow the next posts for all the ranges of numbers); for example, let's apply it for 1000014 * 1000006
1000014 = 1000000 + 14; keep 14 in your mind
1000006 = 1000000 + 6; keep 6 in your mind
then:
1000014 * 1000006 = (1000014+6) & ... & (14*6)
1000014 * 1000006 = 1000020 & 0000 & 84 = 1000020000084
Now, before starting the next post on "Race a Calculator", do the following exercises without a pen and paper, or any calculator; just in the head:
1) 999 * 999 (review Race a Calculator! [Part One] if you cannot remember the trick)
2) 1001 * 1001
3) 997 * 993
4) 10005 * 10011
5) 9995 * 9998
6) 10100 * 10004
7) 9999993 * 9999993
8) 10000101 * 10000004
[continued ...]
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