Question 1204619: Given the set {1,2,3,5,8,13,21,34} which integers between 30 and 50 cannot be written as a number from the set on it’s own, or as the sum of either two or three numbers from the given set.
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Solved at this forum several years ago under this link
https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1147569.html
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
I'm not sure why I included 4 in my previous answer, but here's a rewrite.
When considering 3 items from the set {1,2,3,5,8,13,21,34} we could have the following examples
30 = 1+8+21
31 = 2+8+21
32 = 3+8+21
NOT able to form 33
34 = 5+8+21
35 = 1+13+21
36 = 2+13+21
37 = 1+2+34
38 = 1+3+34
39 = 2+3+34
40 = 1+5+34
41 = 2+5+34
42 = 3+5+34
43 = 1+8+34
44 = 2+8+34
45 = 3+8+34
NOT able to form 46
47 = 5+8+34
48 = 1+13+34
49 = 2+13+34
50 = 3+13+34
possible sums = 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50
sums not able to be formed = 33, 46
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Or if we consider 2 items from the set {1,2,3,5,8,13,21,34}, then,
34 = 13+21
35 = 1+34
36 = 2+34
37 = 3+34
39 = 34+5
42 = 34+8
47 = 13+34
possible sums = 34, 35, 36, 37, 39, 42, and 47
sums we cannot form = 30, 31, 32, 33, 38, 40, 41, 43, 44, 45, 46, 48, 49, and 50
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Answer: The only sums we cannot reach are 33 and 46 when we're able to add 2 or 3 items from the set {1,2,3,5,8,13,21,34}
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
This problem is DIFFERENT than the one in the link referenced by tutor @ikleyn. In this problem, the number 4 is not in the given set.
I also suspect that, although not stated specifically, any number from the set can be used only once.
So the response from the other tutor is not valid, for at least one and maybe two reasons.
So....
30 = 21+8+1
31 = 21+8+2
32 = 21+8+3
33 NO single number; and NO sum of either 2 or 3 different numbers
34 = 34
35 = 34+1
36 = 34+2
37 = 34+3
38 = 34+3+1
39 = 34+3+2
40 = 34+5+1
41 = 34+5+2
42 = 34+5+3
43 = 34+8+1
44 = 34+8+2
45 = 34+8+3
46 NO single number; and NO sum of either 2 or 3 different numbers
47 = 34+13
48 = 34+13+1
49 = 34+13+2
50 = 34+13+3
ANSWER: 33 and 46
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