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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
 #1
avatar+23070 
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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

 

laugh

 Jul 25, 2019

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