SOLUTION: professor B. neat decided to clean out her supply cabinet. She found a balance and set of 63 weights (1 gram , 2 grams, 3 grams, and all the rest, through 63 grams) We dont need al

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Question 599687: professor B. neat decided to clean out her supply cabinet. She found a balance and set of 63 weights (1 gram , 2 grams, 3 grams, and all the rest, through 63 grams) We dont need all these weights, she said. I can get get rid of most of them . If i keep 1 gram and 2 grams , I can get rid of the 3-gram weight, since I can weigh 3 grams using the 1-gram and the 2-gram weights together. What is the fewest number of weights the professor can keep and still be able to weigh items from 1 to 63 grams?
which ones are they?
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Keep only the weights which are a power of 2 grams.

20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32

 1 = 1
 2 = 2
 3 = 1+2
 4 = 4
 5 = 1+4
 6 = 2+4
 7 = 1+2+4
 8 = 8
 9 = 8+1
10 = 8+2
11 = 8+2+1
12 = 8+4
13 = 8+4+1
14 = 8+4+2
15 = 8+4+2+1
16 = 16
17 = 16+1
18 = 16+2
19 = 16+2+1
20 = 16+4
21 = 16+4+1
22 = 16+4+2
23 = 16+4+2+1
24 = 16+8
25 = 16+8+1
26 = 16+8+2
27 = 16+8+2+1
28 = 16+8+4
29 = 16+8+4+1
30 = 16+8+4+2
31 = 16+8+4+2+1
32 = 32
33 = 32+1
34 = 32+2
35 = 32+1+2
36 = 32+4
37 = 32+1+4
38 = 32+2+4
39 = 32+1+2+4
40 = 32+8
41 = 32+8+1
42 = 32+8+2
43 = 32+8+2+1
44 = 32+8+4
45 = 32+8+4+1
46 = 32+8+4+2
47 = 32+8+4+2+1
48 = 32+16
49 = 32+16+1
50 = 32+16+2
51 = 32+16+2+1
52 = 32+16+4
53 = 32+16+4+1
54 = 32+16+4+2
55 = 32+16+4+2+1
56 = 32+16+8
57 = 32+16+8+1
58 = 32+16+8+2
59 = 32+16+8+2+1
60 = 32+16+8+4
61 = 32+16+8+4+1
62 = 32+16+8+4+2
63 = 32+16+8+4+2+1

Edwin
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