991 * 999 = 990009
992 * 999 = 991008
993 * 999 = 992007
...
991 * 998 = 989018
992 * 998 = 990016
993 * 998 = 991014
...
Here is a pattern that makes it easy to calculate them quickly in head:
991 * 999 = 990009
991 = 1000 - 9; keep 9 in your mind
999 = 1000 - 1; keep 1 in your mind
and now:
991 * 999 = (991-1) & ...(1*9)
= 990 & ...9
as ...9 must be a 3-digit number we concatenate 00 to it; so the result will be:
= 990 & 00 & 9 = 990009
This pattern can be applied for the other multiplications:
992 * 999 = 991008
992 = 1000 - 8; keep 8 in your mind
999 = 1000 - 1; keep 1 in your mind
and now:
992 * 999 = (992-1) & 00 & (1*8)
= 991008
Let's try 994 * 996:
994 = 1000 - 6; keep 6 in your mind
996 = 1000 - 4; keep 4 in your mind
then:
994 * 996 = (994-4) & ... & (6*4)
994 * 996 = 990024
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 99994 * 99996:
99994 = 100000 - 6; keep 6 in your mind
99996 = 100000 - 4; keep 4 in your mind
then:
99994 * 99996 = (99994-4) & ... & (6*4)
99994 * 99996 = 99990 & 000 & 24 = 9999000024
[continued ...]
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