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# Help

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Zan has created this iterative rule for generating sequences of whole numbers:

1) If a number is 25 or less, double the number.

2) If a number is greater than 25, subtract 12 from it.

Let F be the first number in a sequence generated by the rule above. F is a "sweet number" if 16 is not a term in the sequence that starts with F. How many of the whole numbers 1 through 50 are "sweet numbers"?

Jul 24, 2019

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+25485
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Zan has created this iterative rule for generating sequences of whole numbers:

1) If a number is 25 or less, double the number.
2) If a number is greater than 25, subtract 12 from it.

Let F be the first number in a sequence generated by the rule above.

F is a "sweet number" if 16 is not a term in the sequence that starts with F.
How many of the whole numbers 1 through 50 are "sweet numbers"?

1 -> 2 -> 4 -> 8 -> 16
2 -> 4 -> 8 -> 16
3 -> 6 -> 12 -> 24 -> 48 -> 36 -> 24 sweet number
4 -> 8 -> 16
5 -> 10 -> 20 -> 40 -> 28 -> 16
6 -> 12 -> 24 -> 48 -> 36 -> 24 sweet number
7 -> 14 -> 28 -> 16
8 -> 16
9 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
10 -> 20 -> 40 -> 28 -> 16
11 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
12 -> 24 -> 48 -> 36 -> 24 sweet number
13 -> 26 -> 14 -> 28 -> 16
14 -> 28 -> 16
15 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
16 -> 32 -> 20 -> 40 -> 28 -> 16
17 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
18 -> 36 -> 24 -> 48 -> 36 sweet number
19 -> 38 -> 26 -> 14 -> 28 -> 16
20 -> 40 -> 28 -> 16
21 -> 42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
23 -> 46 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
24 -> 48 -> 36 -> 24 sweet number
25 -> 50 -> 38 -> 26 -> 14 -> 28 -> 16
26 -> 14 -> 28 -> 16
27 -> 15 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
28 -> 16
29 -> 17 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
31 -> 19 -> 38 -> 26 -> 14 -> 28 -> 16
32 -> 20 -> 40 -> 28 -> 16
33 -> 21 -> 42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
35 -> 23 -> 46 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
36 -> 24 -> 48 -> 36 sweet number
37 -> 25 -> 50 -> 38 -> 26 -> 14 -> 28 -> 16
38 -> 26 -> 14 -> 28 -> 16
39 -> 27 -> 15 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
40 -> 28 -> 16
41 -> 29 -> 17 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
43 -> 31 -> 19 -> 38 -> 26 -> 14 -> 28 -> 16
44 -> 32 -> 20 -> 40 -> 28 -> 16
45 -> 33 -> 21 -> 42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
46 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
47 -> 35 -> 23 -> 46 -> 34 -> 22 -> 44 -> 32 -> 20 -> 40 -> 28 -> 16
48 -> 36 -> 24 -> 48 sweet number
49 -> 37 -> 25 -> 50 -> 38 -> 26 -> 14 -> 28 -> 16
50 -> 38 -> 26 -> 14 -> 28 -> 16

There are 16 sweet number:
3 -> 6 -> 12 -> 24 -> 48 -> 36 -> 24 sweet number
6 -> 12 -> 24 -> 48 -> 36 -> 24 sweet number
9 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
12 -> 24 -> 48 -> 36 -> 24 sweet number
15 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
18 -> 36 -> 24 -> 48 -> 36 sweet number
21 -> 42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
24 -> 48 -> 36 -> 24 sweet number
27 -> 15 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
33 -> 21 -> 42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
36 -> 24 -> 48 -> 36 sweet number
39 -> 27 -> 15 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
45 -> 33 -> 21 -> 42 -> 30 -> 18 -> 36 -> 24 -> 48 -> 36 sweet number
48 -> 36 -> 24 -> 48 sweet number

Jul 25, 2019