Knapsack: 1,3,5,10,20

33, 18, 20, 1, 31, 20, 30, 33

Code	Binary	LETTER
33	01011	K
18	01110	N
20	00001	A
1	10000	P
31	10011	S
20	00001	A
30	00011	C
33	01011	K

Knapsack: 1,2,3,4,5

1, 5, 14, 4, 5, 8, 10, 5, 4, 7, 9

Code	Binary	LETTER(S)
1	10000	P
5	10010 or 01100 or 00001	R, L, A
14	01111	O
4	10100 or 00010	T, B
5	10010 or 01100 or 00001	R, L, A
8	11001 or 10110 or 00101	X, V, E
10	10011 or 01101	S, M
5	10010 or 01100 or 00001	R, L, A
4	10100 or 00010	T, B
7	11010 or 00110 or 01001	Z, F, I
9	01110 or 10101 or 00011	N, U, C

The superincreasing series 1,2,4,8,... enables you to generate all integers in one (and only one) way - there is a one to one mapping so every number is a unique combination of some of the digits in the sequence.

In any superincreasing series 1,3,5,10,20 it is not possible to make all the integers but there is a one-to-one mapping from the combinations of sums of numbers in the sequence and the possible numbers soyou can still decode using the subtraction method.

Because the mappings for a non-superincreasing series are not one-to one then the subtraction method will not work (you do not know what to subtract first).