Given A = {1, 2, 3, 5, 8,13, 21, 34, 55}, how many of the numbers between 3 and 89 cannot be written as the sum of two elements of the set?
I think that you have to add them all up sequentially, that is: 1+2; 1+3; 1+5.....etc. When you finish with 1 then you start with 2: 2+3; 2+5; 2+8.......and so on. When you do that, this is what you will get:
(3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 21, 22, 23, 24, 26, 29, 34, 35, 36, 37, 39, 42, 47, 55, 56, 57, 58, 60, 63, 68, 76, 89). From this list, you can easily tell that you cannot make 12 or 17 or 19 or 20.......and so on. Just go through the entire list and write down the numbers that are not on the list, all the way up to 89. The list has 36 numbers, which means you have to write down: 89 - 36 =53 numbers that are not on the list. Make sure to count them to ensure that you have written down all 53 numbers.
