Question 10
Start with the number 2. At each turn, you may either add 4 to the current number or multiply the current number by 3. For example, it is possible to reach exactly 82 in 18 turns as shown below:
$$(2+4)\times3+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4=82.$$
What is the minimum number of turns required to get 82?
$$(2+4)\times3+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4=82.$$
What is the minimum number of turns required to get 82?