Understanding the Rules
The transformation rules given are as follows:
- If x is odd: x = 3x + 1
- If x is even: x = x ÷ 2
Starting with x = 27, we will apply these rules iteratively until we reach a final result.
Step 1: Initial Value
- Start with x = 27 (which is odd).
Step 2: Apply Odd Rule
- Since 27 is odd, apply the odd rule:
x = 3(27) + 1 = 81 + 1 = 82
Step 3: Apply Even Rule
- Now, x = 82 (which is even).
Apply the even rule:
x = 82 ÷ 2 = 41
Step 4: Apply Odd Rule Again
- x = 41 (which is odd).
Apply the odd rule:
x = 3(41) + 1 = 123 + 1 = 124
Step 5: Continue with Even Rule
- x = 124 (which is even).
Apply the even rule:
x = 124 ÷ 2 = 62
Step 6: Repeat the Process
- x = 62 (even):
x = 62 ÷ 2 = 31
- x = 31 (odd):
x = 3(31) + 1 = 94
- x = 94 (even):
x = 94 ÷ 2 = 47
- x = 47 (odd):
x = 3(47) + 1 = 142
- x = 142 (even):
x = 142 ÷ 2 = 71
- x = 71 (odd):
x = 3(71) + 1 = 214
- x = 214 (even):
x = 214 ÷ 2 = 107
- x = 107 (odd):
x = 3(107) + 1 = 322
- x = 322 (even):
x = 322 ÷ 2 = 161
- x = 161 (odd):
x = 3(161) + 1 = 484
- x = 484 (even):
x = 484 ÷ 2 = 242
- x = 242 (even):
x = 242 ÷ 2 = 121
- x = 121 (odd):
x = 3(121) + 1 = 364
- x = 364 (even):
x = 364 ÷ 2 = 182
- x = 182 (even):
x = 182 ÷ 2 = 91
- x = 91 (odd):
x = 3(91) + 1 = 274
- x = 274 (even):
x = 274 ÷ 2 = 137
- x = 137 (odd):
x =