Suppose you have a list of all consecutive even number from 2 to 2012
If you take away all the multiples of three, how many numbers will be left?
We have this list:
2, 4, 6, ... , 2008, 2010, 2012
We can tell how many numbers this is by dividing every one by 2
1, 2, 3, ... , 1004, 1005, 1006
So there are 1006 numbers to start with.
We find out what the largest number in the list is that is a multiple
of 3.
Since 2012÷3 = 670.666... it is 670×3 = 2010
So we take the following away from the first list:
6, 12, 18, ... , 1998, 2004, 2010
We can tell how many numbers this is by dividing every one by 6
1, 2, 3, ..., 333, 334, 335
So there are 335 numbers to take away.
So we take 335 away from 1006 and get 671 numbers left.
Edwin
